Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
252 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10588767 | C2 | semidirect |
| 4. #10588359 | C2 | semidirect |
| 5. #10588224 | C2 | semidirect |
| 7. #10588135 | C2 | semidirect |
| 83. C8×C9 | SD16 | semidirect |
| 196. C9 | #1686 | semidirect |
| 217. C8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#492 | 2 |
| #10588767 | 2 |
| #10588752 | 2 |
| #10588359 | 2 |
| #10588224 | 2 |
| #10588221 | 2 |
| #10588135 | 2 |
| #71273 | 3 |