Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 186 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. Q82×C9 | C2 | semidirect |
| 3. #10588773 | C2 | semidirect |
| 4. #10588769 | C2 | semidirect |
| 5. #10588710 | C2 | semidirect |
| 6. C4×#3675 | C2 | semidirect |
| 7. Q8×C9⋊C8 | C2 | semidirect |
| 71. Q8×C9 | SD16 | semidirect |
| 72. Q8×C9 | #41 | semidirect |
| 86. Q82 | D9 | semidirect |
| 191. C9 | #3362 | semidirect |
| 195. Q8 | #3675 | semidirect |
| 196. Q8 | #3701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C9 | 2 |
| #10589679 | 2 |
| #10588773 | 2 |
| #10588769 | 2 |
| #10588710 | 2 |
| C4×#3675 | 2 |
| Q8×C9⋊C8 | 2 |
| #83703 | 3 |