Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
666 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 130 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. C9×#518 | C2 | semidirect |
| 3. C2×#63391 | C2 | semidirect |
| 4. #10588682 | C2 | semidirect |
| 5. #10588208 | C2 | semidirect |
| 14. #63502 | C4 | semidirect |
| 38. C2×D36 | C2×C4 | semidirect |
| 39. C9×C4⋊C4 | D4 | semidirect |
| 44. C4×Dic9 | C2×C4 | semidirect |
| 85. #518 | D9 | semidirect |
| 188. C4⋊C4 | #611 | semidirect |
| 210. C9 | #1887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#518 | 2 |
| C2×#63502 | 2 |
| C2×#63391 | 2 |
| #10588682 | 2 |
| #10588208 | 2 |
| #71650 | 3 |