Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×Q16×D9 | C2 | semidirect |
| 2. C2×C9×SD32 | C2 | semidirect |
| 4. C2×#63386 | C2 | semidirect |
| 5. #10588241 | C2 | semidirect |
| 6. (C2×D9)⋊C16 | C2 | semidirect |
| 7. #10588180 | C2 | semidirect |
| 41. C9×Q16 | D4 | semidirect |
| 52. Dic36 | D4 | semidirect |
| 94. C2×SD32 | D9 | semidirect |
| 129. C2×D9 | SD32 | semidirect |
| 190. Q16 | #611 | semidirect |
| 214. C9 | #2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D9 | 2 |
| C2×C9×SD32 | 2 |
| #10588837 | 2 |
| C2×#63386 | 2 |
| #10588241 | 2 |
| (C2×D9)⋊C16 | 2 |
| #10588180 | 2 |
| #71483 | 3 |