Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
282 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 282 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 |
|---|---|---|
| 1. #10588530 | C2 | semidirect |
| 3. #10588375 | C2 | semidirect |
| 4. C8×D36 | C2 | semidirect |
| 5. C9×#334 | C2 | semidirect |
| 6. #10588163 | C2 | semidirect |
| 7. #10588161 | C2 | semidirect |
| 80. D36 | SD16 | semidirect |
| 88. C8×C9 | D8 | semidirect |
| 94. #334 | D9 | semidirect |
| 208. C9 | #1665 | semidirect |
| 231. C8 | D72 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588530 | 2 |
| #10588527 | 2 |
| #10588375 | 2 |
| C8×D36 | 2 |
| C9×#334 | 2 |
| #10588163 | 2 |
| #10588161 | 2 |
| #68536 | 3 |