Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
258 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 74 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. D8×Dic9 | C2 | semidirect |
| 3. #10588552 | C2 | semidirect |
| 4. C9×#357 | C2 | semidirect |
| 5. #10588186 | C2 | semidirect |
| 6. #10588179 | C2 | semidirect |
| 7. #10588167 | C2 | semidirect |
| 16. #63385 | C4 | semidirect |
| 33. C9×D8 | C2×C4 | semidirect |
| 42. D72 | C2×C4 | semidirect |
| 44. C9⋊C16 | C2×C4 | semidirect |
| 79. #357 | D9 | semidirect |
| 151. D8 | C4×D9 | semidirect |
| 174. C9 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic9 | 2 |
| C2×#63385 | 2 |
| #10588552 | 2 |
| C9×#357 | 2 |
| #10588186 | 2 |
| #10588179 | 2 |
| #10588167 | 2 |
| #69177 | 3 |