Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
348 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×#63378 | C2 | semidirect |
| 3. C2×#63371 | C2 | semidirect |
| 4. #10588241 | C2 | semidirect |
| 5. #10588239 | C2 | semidirect |
| 9. C9×#135 | C4 | semidirect |
| 33. C9×Q16 | C2×C4 | semidirect |
| 36. C9×D8 | C2×C4 | semidirect |
| 114. #135 | Dic9 | semidirect |
| 156. Q16 | C2×Dic9 | semidirect |
| 159. D8 | C2×Dic9 | semidirect |
| 179. C9 | #2139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#135 | 2 |
| C2×#63378 | 2 |
| C2×#63371 | 2 |
| #10588241 | 2 |
| #10588239 | 2 |
| #72078 | 3 |