Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
255 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10588588 | C2 | semidirect |
| 2. #10588380 | C2 | semidirect |
| 3. #10588377 | C2 | semidirect |
| 4. C9×#364 | C2 | semidirect |
| 5. #10588193 | C2 | semidirect |
| 34. D72 | D4 | semidirect |
| 38. Dic36 | D4 | semidirect |
| 70. #364 | D9 | semidirect |
| 152. C9 | #2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588588 | 2 |
| #10588380 | 2 |
| #10588377 | 2 |
| C9×#364 | 2 |
| #10588193 | 2 |
| #69305 | 3 |