Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
363 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 78. #634 | Q16 | semidirect |
| 228. C32 | #1670 | semidirect |
| 262. C3 | #68587 | semidirect |
| 263. C3 | #71308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#634 | 2 |
| C3×#4699 | 2 |
| #10590307 | 2 |
| C3×#4458 | 2 |
| #10589092 | 2 |
| #71308 | 3 |
| #68587 | 3 |