Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
4632 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C4×D23 | C2 | semidirect |
| 3. C22×C22⋊Dic23 | C2 | semidirect |
| 4. C22×(C2×D23)⋊C4 | C2 | semidirect |
| 5. C2×C22⋊C4×D23 | C2 | direct (N × H) |
| 6. C22×C22⋊C4×C23 | C2 | semidirect |
| 9. C24×D23 | C4 | semidirect |
| 13. C23×C4×C23 | C22 | semidirect |
| 14. C23×Dic23 | C22 | semidirect |
| 16. C22×C4×D23 | C22 | semidirect |
| 17. C2×C22⋊C4×C23 | C22 | semidirect |
| 18. C2×C22⋊Dic23 | C22 | semidirect |
| 19. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 20. C22⋊C4×D23 | C22 | direct (N × H) |
| 22. C24×C23 | C2×C4 | semidirect |
| 29. C23×D23 | C2×C4 | semidirect |
| 30. C23×D23 | C2×C4 | semidirect |
| 36. C22×C4×C23 | C23 | semidirect |
| 38. C22×Dic23 | C23 | semidirect |
| 40. C2×C4×D23 | C23 | semidirect |
| 41. C22⋊C4×C23 | C23 | semidirect |
| 42. C22⋊Dic23 | C23 | semidirect |
| 43. (C2×D23)⋊C4 | C23 | semidirect |
| 47. C23×C23 | C22×C4 | semidirect |
| 55. C22×D23 | C22⋊C4 | direct (N × H) |
| 57. C22×D23 | C22×C4 | semidirect |
| 58. C22×D23 | C22×C4 | semidirect |
| 63. C2×C4×C23 | C24 | semidirect |
| 65. C2×Dic23 | C24 | semidirect |
| 70. C22×C23 | C2×C22⋊C4 | semidirect |
| 72. C22×C23 | C23×C4 | semidirect |
| 78. C2×D23 | C2×C22⋊C4 | direct (N × H) |
| 80. C2×D23 | C23×C4 | semidirect |
| 89. C22×C22⋊C4 | D23 | direct (N × H) |
| 91. C2×C23 | C22×C22⋊C4 | semidirect |
| 95. D23 | C22×C22⋊C4 | direct (N × H) |
| 105. C23×C4 | C2×D23 | semidirect |
| 109. C2×C22⋊C4 | C2×D23 | direct (N × H) |
| 110. C23 | C23×C22⋊C4 | semidirect |
| 122. C24 | C4×D23 | semidirect |
| 130. C22×C4 | C22×D23 | semidirect |
| 133. C22⋊C4 | C22×D23 | direct (N × H) |
| 148. C23 | C2×C4×D23 | semidirect |
| 156. C2×C4 | C23×D23 | semidirect |
| 166. C22 | C22⋊C4×D23 | direct (N × H) |
| 168. C22 | C22×C4×D23 | semidirect |
| 176. C2 | C2×C22⋊C4×D23 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D23 | 2 |
| C23×C4×D23 | 2 |
| C22×C22⋊Dic23 | 2 |
| C22×(C2×D23)⋊C4 | 2 |
| C2×C22⋊C4×D23 | 2 |
| C22×C22⋊C4×C23 | 2 |
| C23×C22⋊C4 | 23 |