Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #13092139 | C2 | semidirect |
| 5. C8×C23⋊C8 | C2 | semidirect |
| 6. C8×C23⋊C8 | C2 | semidirect |
| 7. C23×#322 | C2 | semidirect |
| 34. #67262 | C8 | semidirect |
| 48. C8×C23 | C2×C8 | semidirect |
| 50. C23⋊C8 | C2×C8 | semidirect |
| 51. C23⋊C8 | M16 | semidirect |
| 67. #322 | D23 | semidirect |
| 87. C23 | C8×M16 | semidirect |
| 118. C8 | C8×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092468 | 2 |
| C4×#67262 | 2 |
| C4×C8×D23 | 2 |
| #13092139 | 2 |
| C8×C23⋊C8 | 2 |
| C23×#322 | 2 |
| C8×M16 | 23 |