Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
798 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 154 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. #10589818 | C2 | semidirect |
| 2. D9×#127 | C2 | semidirect |
| 3. C9×#493 | C2 | semidirect |
| 4. #10588836 | C2 | semidirect |
| 5. #10588830 | C2 | semidirect |
| 6. #10588755 | C2 | semidirect |
| 7. #10588750 | C2 | semidirect |
| 8. #10588376 | C2 | semidirect |
| 9. #10588367 | C2 | semidirect |
| 15. C2×C9×D8 | C22 | semidirect |
| 17. C9×#127 | C22 | semidirect |
| 25. D4×Dic9 | C22 | semidirect |
| 26. C2×#3673 | C22 | semidirect |
| 29. #63431 | C22 | semidirect |
| 30. C4×C8×C9 | C22 | semidirect |
| 31. #63392 | C22 | semidirect |
| 32. #63380 | C22 | semidirect |
| 34. Dic9⋊C8 | C22 | semidirect |
| 35. C4×C9⋊C8 | C22 | semidirect |
| 136. C4×D9 | D8 | semidirect |
| 143. #493 | D9 | semidirect |
| 210. C2×D8 | C2×D9 | semidirect |
| 217. #127 | C2×D9 | semidirect |
| 229. C4×C8 | C2×D9 | semidirect |
| 327. C9 | #3205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589818 | 2 |
| D9×#127 | 2 |
| C9×#493 | 2 |
| #10588836 | 2 |
| #10588830 | 2 |
| #10588755 | 2 |
| #10588750 | 2 |
| #10588376 | 2 |
| #10588367 | 2 |
| #81785 | 3 |