Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10588361 | C2 | semidirect |
| 5. C9×#335 | C2 | semidirect |
| 6. #10588161 | C2 | semidirect |
| 7. #10588158 | C2 | semidirect |
| 87. #335 | D9 | semidirect |
| 186. C9 | #1683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588530 | 2 |
| #10588526 | 2 |
| C8×D36 | 2 |
| #10588361 | 2 |
| C9×#335 | 2 |
| #10588161 | 2 |
| #10588158 | 2 |
| #68581 | 3 |