Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 86 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. C22×C9×Q16 | C2 | semidirect |
| 2. C2×#63387 | C2 | semidirect |
| 4. #10588241 | C2 | semidirect |
| 5. #10588226 | C2 | semidirect |
| 33. C9×Q16 | D4 | semidirect |
| 70. C22×Q16 | D9 | semidirect |
| 95. C22×C9 | SD32 | semidirect |
| 148. Q16 | #611 | semidirect |
| 168. C9 | #2185 | semidirect |
| 196. C22 | #63387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Q16 | 2 |
| C2×#63387 | 2 |
| #10588796 | 2 |
| #10588241 | 2 |
| #10588226 | 2 |
| #72063 | 3 |