Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
258 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #10588365 | C2 | semidirect |
| 4. C9×#335 | C2 | semidirect |
| 5. #10588161 | C2 | semidirect |
| 57. D36 | Q16 | semidirect |
| 69. #335 | D9 | semidirect |
| 154. C9 | #1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588530 | 2 |
| C8×D36 | 2 |
| #10588365 | 2 |
| C9×#335 | 2 |
| #10588161 | 2 |
| #68577 | 3 |