Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
489 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10588891 | C2 | semidirect |
| 3. #10588887 | C2 | semidirect |
| 4. #10588214 | C2 | semidirect |
| 7. C22×D4×C9 | C4 | semidirect |
| 11. C9×#121 | C4 | semidirect |
| 13. C2×C9×C4⋊C4 | C4 | semidirect |
| 18. C9⋊#95 | C22 | semidirect |
| 20. #63389 | C22 | semidirect |
| 145. C22×D4 | Dic9 | semidirect |
| 150. #121 | Dic9 | semidirect |
| 152. C2×C4⋊C4 | Dic9 | semidirect |
| 241. C9 | #1510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#121 | 2 |
| #10588891 | 2 |
| #10588887 | 2 |
| #10588214 | 2 |
| #71674 | 3 |