Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 4. #10588805 | C2 | semidirect |
| 5. #10588657 | C2 | semidirect |
| 6. C9×#343 | C2 | semidirect |
| 7. #10588235 | C2 | semidirect |
| 22. #63384 | C4 | semidirect |
| 50. C9×M16 | C2×C4 | semidirect |
| 65. C4×Dic9 | C2×C4 | semidirect |
| 119. #343 | D9 | semidirect |
| 240. M16 | C4×D9 | semidirect |
| 274. C9 | #1860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589606 | 2 |
| C2×#63384 | 2 |
| #10588815 | 2 |
| #10588805 | 2 |
| #10588657 | 2 |
| C9×#343 | 2 |
| #10588235 | 2 |
| #69003 | 3 |