Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1200 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1200 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×#518 | C2 | semidirect |
| 3. #10589900 | C2 | semidirect |
| 4. #10588686 | C2 | semidirect |
| 5. C2×#63365 | C2 | semidirect |
| 11. C2×#3699 | C4 | semidirect |
| 12. C2×D4×D9 | C4 | semidirect |
| 15. C9×#117 | C22 | semidirect |
| 16. C2×C9×C22⋊C4 | C22 | semidirect |
| 17. C2×#3676 | C22 | semidirect |
| 19. #63488 | C22 | semidirect |
| 20. #63365 | C22 | semidirect |
| 27. C23×D9 | C2×C4 | semidirect |
| 35. C2×#611 | C2×C4 | semidirect |
| 38. C22×Dic9 | C2×C4 | semidirect |
| 43. C2×D36 | C2×C4 | semidirect |
| 44. C2×C4×D9 | C2×C4 | semidirect |
| 45. C2×Dic18 | C2×C4 | semidirect |
| 95. #518 | D9 | semidirect |
| 151. #117 | C2×D9 | semidirect |
| 153. C2×C22⋊C4 | C2×D9 | semidirect |
| 228. C9 | #2883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63710 | 2 |
| C9×#518 | 2 |
| #10589900 | 2 |
| #10588686 | 2 |
| C2×#63365 | 2 |
| #82546 | 3 |