Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 6. #10593532 | C2 | semidirect |
| 7. #10593532 | C2 | semidirect |
| 8. C8×PSU(3,𝔽2) | C2 | semidirect |
| 54. C32×M16 | Q8 | semidirect |
| 55. #3748 | Q8 | semidirect |
| 56. #3743 | Q8 | semidirect |
| 154. M16 | PSU(3,𝔽2) | semidirect |
| 182. C32 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596542 | 2 |
| #10593775 | 2 |
| M16×#157 | 2 |
| #10593540 | 2 |
| C2×#63744 | 2 |
| #10593532 | 2 |
| C8×PSU(3,𝔽2) | 2 |
| #2962 | 9 |