Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×D4×Dic23 | C2 | semidirect |
| 3. C2×#10625064 | C2 | semidirect |
| 4. #13092497 | C2 | direct (N × H) |
| 5. C2×#10624989 | C2 | semidirect |
| 6. C2×#10625003 | C2 | semidirect |
| 7. C2×C8×Dic23 | C2 | semidirect |
| 8. C2×C23×#102 | C2 | semidirect |
| 17. D4×Dic23 | C22 | semidirect |
| 18. C2×#67272 | C4 | semidirect |
| 25. #10625064 | C22 | semidirect |
| 26. C23×#102 | C22 | semidirect |
| 27. #10625003 | C22 | semidirect |
| 28. C8×Dic23 | C22 | semidirect |
| 29. #10624989 | C22 | semidirect |
| 34. C2×D4×C23 | C2×C4 | semidirect |
| 45. C2×D92 | C2×C4 | semidirect |
| 54. #67272 | C2×C4 | semidirect |
| 60. C2×C23⋊C8 | C2×C4 | semidirect |
| 73. D4×C23 | C22×C4 | semidirect |
| 84. C2×Dic23 | D8 | semidirect |
| 89. D92 | C22×C4 | semidirect |
| 92. C23⋊C8 | C22×C4 | semidirect |
| 112. Dic23 | C2×D8 | semidirect |
| 119. C2×#102 | D23 | semidirect |
| 122. C2×C23 | C4×D8 | semidirect |
| 146. #102 | C2×D23 | semidirect |
| 148. C23 | C2×C4×D8 | semidirect |
| 157. C2×D4 | C4×D23 | semidirect |
| 195. D4 | C2×C4×D23 | semidirect |
| 233. C2 | #13092497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67272 | 2 |
| C2×D4×Dic23 | 2 |
| C2×#10625064 | 2 |
| #13092497 | 2 |
| C2×#10624989 | 2 |
| C2×#10625003 | 2 |
| C2×C8×Dic23 | 2 |
| C2×C23×#102 | 2 |
| C2×C4×D8 | 23 |