Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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. C24×Dic23 | C2 | semidirect |
| 3. C2×#10625057 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic23 | C2 | semidirect |
| 5. C22×(C2×D23)⋊C4 | C2 | semidirect |
| 6. C22×C22⋊C4×C23 | C2 | semidirect |
| 15. C23×Dic23 | C22 | semidirect |
| 16. C2×C22⋊C4×C23 | C22 | semidirect |
| 17. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 18. C2×C4⋊Dic23 | C22 | semidirect |
| 19. #10625057 | C22 | direct (N × H) |
| 36. C22×Dic23 | C23 | semidirect |
| 37. C22⋊C4×C23 | C23 | semidirect |
| 38. (C2×D23)⋊C4 | C23 | semidirect |
| 39. C4⋊Dic23 | C23 | semidirect |
| 62. C22×C23 | #123 | semidirect |
| 78. C22×C22⋊C4 | D23 | semidirect |
| 80. C2×C23 | C2×#123 | semidirect |
| 96. C2×C22⋊C4 | C2×D23 | semidirect |
| 97. C23 | C22×#123 | semidirect |
| 117. C22⋊C4 | C22×D23 | semidirect |
| 142. C22 | #10625057 | direct (N × H) |
| 152. C2 | C2×#10625057 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D23 | 2 |
| C24×Dic23 | 2 |
| C2×#10625057 | 2 |
| C22×C4⋊Dic23 | 2 |
| C22×(C2×D23)⋊C4 | 2 |
| C22×C22⋊C4×C23 | 2 |
| C22×#123 | 23 |