Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 58 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. #10593752 | C2 | semidirect |
| 3. #10590171 | C2 | semidirect |
| 4. C8×#622 | C2 | semidirect |
| 5. #10590160 | C2 | semidirect |
| 48. #622 | D8 | semidirect |
| 49. C32×C8 | M16 | semidirect |
| 122. C32 | #1589 | semidirect |
| 137. C8 | #3788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593752 | 2 |
| #10592571 | 2 |
| #10590171 | 2 |
| C8×#622 | 2 |
| #10590160 | 2 |
| #1589 | 9 |