Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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×#67272 | C2 | semidirect |
| 2. C2×#10625078 | C2 | semidirect |
| 3. #13092986 | C2 | semidirect |
| 4. #13092984 | C2 | semidirect |
| 5. #13092669 | C2 | semidirect |
| 6. #13092652 | C2 | semidirect |
| 7. #13092453 | C2 | semidirect |
| 8. #13092423 | C2 | semidirect |
| 9. C23×#418 | C2 | semidirect |
| 17. #10625109 | C22 | semidirect |
| 25. C2×#67262 | C22 | semidirect |
| 26. C2×C8×D23 | C22 | semidirect |
| 27. #10625066 | C22 | semidirect |
| 31. C23×#102 | C22 | semidirect |
| 32. #10625003 | C22 | semidirect |
| 33. #10624990 | C22 | semidirect |
| 34. #10624989 | C22 | semidirect |
| 66. C2×C23⋊C8 | D4 | semidirect |
| 128. #418 | D23 | semidirect |
| 159. #102 | C2×D23 | semidirect |
| 160. C23 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67272 | 2 |
| C2×#10625078 | 2 |
| #13092986 | 2 |
| #13092984 | 2 |
| #13092669 | 2 |
| #13092652 | 2 |
| #13092453 | 2 |
| #13092423 | 2 |
| C23×#418 | 2 |
| #3058 | 23 |