Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2394 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 2394 conjugacy classes of subgroups — too many to draw. Only its 770 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. C23×#622 | C2 | semidirect |
| 4. C2×#64287 | C2 | direct (N × H) |
| 5. C22×#3788 | C2 | semidirect |
| 6. C22×#3787 | C2 | semidirect |
| 14. C2×#3792 | C22 | semidirect |
| 18. C22×#622 | C22 | semidirect |
| 19. #64287 | C22 | direct (N × H) |
| 20. C2×#3788 | C22 | semidirect |
| 21. C2×#3787 | C22 | semidirect |
| 37. #3792 | C23 | semidirect |
| 41. C2×#622 | C23 | semidirect |
| 42. #3788 | C23 | semidirect |
| 43. #3787 | C23 | semidirect |
| 92. C22×C32 | #131 | semidirect |
| 133. C2×C32 | C2×#131 | semidirect |
| 167. C32 | C22×#131 | semidirect |
| 194. C22 | #64287 | direct (N × H) |
| 204. C2 | C2×#64287 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3830 | 2 |
| C22×#3792 | 2 |
| C23×#622 | 2 |
| C2×#64287 | 2 |
| C22×#3788 | 2 |
| C22×#3787 | 2 |
| C22×#131 | 9 |