Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
366 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10589572 | C2 | semidirect |
| 5. #10588237 | C2 | semidirect |
| 6. #10588232 | C2 | semidirect |
| 7. #10588201 | C2 | semidirect |
| 35. C2×Q8×C9 | Q8 | semidirect |
| 37. C2×D4×C9 | Q8 | semidirect |
| 209. C2×Q8 | Dic18 | semidirect |
| 211. C2×D4 | Dic18 | semidirect |
| 251. C9 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589572 | 2 |
| C2×C9×#104 | 2 |
| #10588920 | 2 |
| #10588914 | 2 |
| #10588237 | 2 |
| #10588232 | 2 |
| #10588201 | 2 |
| #70368 | 3 |