Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
600 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 1. C22×C9×D8 | C2 | semidirect |
| 2. C2×#63467 | C2 | semidirect |
| 3. C2×#63386 | C2 | semidirect |
| 4. #10588827 | C2 | direct (N × H) |
| 5. C2×#63385 | C2 | semidirect |
| 6. C2×#63371 | C2 | semidirect |
| 13. C2×C9×D8 | C22 | semidirect |
| 16. #63467 | C22 | semidirect |
| 17. C2×D72 | C22 | semidirect |
| 19. C2×Dic36 | C22 | semidirect |
| 20. #63386 | C22 | semidirect |
| 21. #63385 | C22 | semidirect |
| 22. #63371 | C22 | semidirect |
| 23. C2×C9⋊C16 | C22 | semidirect |
| 50. D72 | C23 | semidirect |
| 53. Dic36 | C23 | semidirect |
| 54. C9⋊C16 | C23 | semidirect |
| 95. C22×D8 | D9 | semidirect |
| 147. C2×D8 | C2×D9 | semidirect |
| 177. C2×C9 | #509 | semidirect |
| 217. C9 | C2×#509 | semidirect |
| 261. C2 | #10588827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D8 | 2 |
| C2×#63467 | 2 |
| C2×#63386 | 2 |
| #10588827 | 2 |
| C2×#63385 | 2 |
| C2×#63371 | 2 |
| C2×#5147 | 3 |