Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
219 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10588876 | C2 | semidirect |
| 3. #10588244 | C2 | semidirect |
| 4. #10588183 | C2 | semidirect |
| 5. C16×Dic9 | C2 | semidirect |
| 9. C9×Q32 | C4 | semidirect |
| 10. C9×SD32 | C4 | semidirect |
| 11. C9×D16 | C4 | semidirect |
| 83. Q32 | Dic9 | semidirect |
| 84. SD32 | Dic9 | semidirect |
| 85. D16 | Dic9 | semidirect |
| 124. C9 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#508 | 2 |
| #10588876 | 2 |
| #10588244 | 2 |
| #10588183 | 2 |
| C16×Dic9 | 2 |
| #71511 | 3 |