Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C2×#63382 | C2 | semidirect |
| 5. C2×#63382 | C2 | semidirect |
| 6. C9×#344 | C2 | semidirect |
| 7. #10588209 | C2 | semidirect |
| 123. #344 | D9 | semidirect |
| 272. C9 | #1915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589847 | 2 |
| #10589628 | 2 |
| #10588814 | 2 |
| C2×#63382 | 2 |
| C9×#344 | 2 |
| #10588209 | 2 |
| #69041 | 3 |