Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3082 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 3082 conjugacy classes of subgroups — too many to draw. Only its 810 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. C22×#3792 | C2 | semidirect |
| 3. C2×#64283 | C2 | direct (N × H) |
| 4. C22×#3788 | C2 | semidirect |
| 5. C22×#3787 | C2 | semidirect |
| 15. C2×#3792 | C22 | semidirect |
| 16. C22×#622 | C22 | semidirect |
| 17. #64283 | C22 | direct (N × H) |
| 18. C2×#3788 | C22 | semidirect |
| 19. C2×#3787 | C22 | semidirect |
| 41. #3792 | C23 | semidirect |
| 42. C2×#622 | C23 | semidirect |
| 43. #3788 | C23 | semidirect |
| 44. #3787 | C23 | semidirect |
| 60. C22×C3⋊D3 | M16 | semidirect |
| 78. #622 | C24 | semidirect |
| 105. C22×C32 | C2×M16 | semidirect |
| 110. C2×C3⋊D3 | C2×M16 | semidirect |
| 156. C2×C32 | C22×M16 | semidirect |
| 159. C3⋊D3 | C22×M16 | semidirect |
| 198. C32 | C23×M16 | semidirect |
| 234. C22 | #64283 | direct (N × H) |
| 246. C2 | C2×#64283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C3⋊D3 | 2 |
| C22×#3792 | 2 |
| C2×#64283 | 2 |
| C22×#3788 | 2 |
| C22×#3787 | 2 |
| C23×M16 | 9 |