Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
348 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 94 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. C9×#358 | C2 | semidirect |
| 5. #10588241 | C2 | semidirect |
| 6. #10588180 | C2 | semidirect |
| 7. #10588169 | C2 | semidirect |
| 13. Q16×D9 | C4 | semidirect |
| 39. C9×Q16 | C2×C4 | semidirect |
| 49. Dic36 | C2×C4 | semidirect |
| 92. #358 | D9 | direct (N × H) |
| 162. D9 | #358 | direct (N × H) |
| 175. Q16 | C4×D9 | semidirect |
| 196. C9 | C2×#358 | 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×C16×D9 | 2 |
| D9×#107 | 2 |
| C9×#358 | 2 |
| #10588241 | 2 |
| #10588180 | 2 |
| #10588169 | 2 |
| D3×#358 | 3 |