Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1107 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1107 conjugacy classes of subgroups — too many to draw. Only its 328 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. C9×#568 | C2 | semidirect |
| 3. #41×Dic9 | C2 | semidirect |
| 4. #10588819 | C2 | semidirect |
| 5. C2×#63384 | C2 | semidirect |
| 8. #63716 | C4 | semidirect |
| 9. #63715 | C4 | semidirect |
| 15. C2×C9×M16 | C22 | semidirect |
| 18. #63488 | C22 | semidirect |
| 19. C2×C4×Dic9 | C22 | semidirect |
| 20. #63384 | C22 | semidirect |
| 21. #63384 | C22 | semidirect |
| 40. #3697 | C2×C4 | semidirect |
| 42. C2×D36 | C2×C4 | semidirect |
| 44. C2×Dic18 | C2×C4 | semidirect |
| 91. #568 | D9 | semidirect |
| 140. C2×M16 | C2×D9 | semidirect |
| 209. C9 | #2901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593139 | 2 |
| C9×#568 | 2 |
| #41×Dic9 | 2 |
| #10588819 | 2 |
| C2×#63384 | 2 |
| #83817 | 3 |