Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
| 3. C2×#63395 | C2 | semidirect |
| 5. #10588229 | C2 | semidirect |
| 68. C22×D9 | Q16 | semidirect |
| 90. C22×Q16 | D9 | semidirect |
| 221. C9 | #2001 | 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×#63508 | 2 |
| C2×#63395 | 2 |
| C2×(C2×D9)⋊C8 | 2 |
| #10588229 | 2 |
| #72071 | 3 |