Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C22×#67290 | C2 | semidirect |
| 2. C2×#10625083 | C2 | semidirect |
| 3. #13092927 | C2 | semidirect |
| 4. #13092580 | C2 | semidirect |
| 5. #13092575 | C2 | semidirect |
| 6. #13092568 | C2 | semidirect |
| 7. #13092559 | C2 | semidirect |
| 8. #13092555 | C2 | semidirect |
| 9. #13092410 | C2 | semidirect |
| 10. C22⋊C8×D23 | C2 | semidirect |
| 11. C23×#447 | C2 | semidirect |
| 20. C2×#67290 | C22 | semidirect |
| 23. C2×D8×C23 | C22 | semidirect |
| 25. #10625109 | C22 | semidirect |
| 28. C2×#67273 | C22 | semidirect |
| 29. C2×#67273 | C22 | semidirect |
| 32. C2×Dic92 | C22 | semidirect |
| 33. C2×C8×D23 | C22 | semidirect |
| 34. #10625068 | C22 | semidirect |
| 35. #10625063 | C22 | semidirect |
| 38. C23×#102 | C22 | semidirect |
| 40. #10625014 | C22 | semidirect |
| 42. (C2×D23)⋊C8 | C22 | semidirect |
| 43. #10624998 | C22 | semidirect |
| 44. #10624992 | C22 | semidirect |
| 70. #67290 | D4 | semidirect |
| 151. C22×C23 | #135 | semidirect |
| 176. #447 | D23 | semidirect |
| 202. C2×D8 | C2×D23 | semidirect |
| 216. #102 | C2×D23 | semidirect |
| 220. C23 | #3002 | semidirect |
| 333. C22 | #10625083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67290 | 2 |
| C2×#10625083 | 2 |
| #13092927 | 2 |
| #13092580 | 2 |
| #13092575 | 2 |
| #13092568 | 2 |
| #13092559 | 2 |
| #13092555 | 2 |
| #13092410 | 2 |
| C22⋊C8×D23 | 2 |
| C23×#447 | 2 |
| #3002 | 23 |