Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. #10588702 | C2 | semidirect |
| 4. #10588360 | C2 | semidirect |
| 5. C9×Q8⋊C8 | C2 | semidirect |
| 6. #10588161 | C2 | semidirect |
| 78. Q8×C9 | SD16 | semidirect |
| 105. Q8⋊C8 | D9 | semidirect |
| 230. C9 | #1651 | semidirect |
| 238. Q8 | #3664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D36 | 2 |
| #10588702 | 2 |
| #10588525 | 2 |
| #10588360 | 2 |
| C9×Q8⋊C8 | 2 |
| #10588161 | 2 |
| #10588136 | 2 |
| #68251 | 3 |