Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 168 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. C9×#576 | C2 | semidirect |
| 2. #10589854 | C2 | semidirect |
| 3. #10588874 | C2 | semidirect |
| 4. #10588873 | C2 | semidirect |
| 5. #10588827 | C2 | semidirect |
| 6. C2×#63385 | C2 | semidirect |
| 7. #10588820 | C2 | semidirect |
| 12. C9×#135 | C22 | semidirect |
| 13. C2×C9×D8 | C22 | semidirect |
| 16. #63467 | C22 | semidirect |
| 17. C2×D72 | C22 | semidirect |
| 18. #63388 | C22 | semidirect |
| 19. #63387 | C22 | semidirect |
| 20. #63386 | C22 | semidirect |
| 21. #63385 | C22 | semidirect |
| 22. #63385 | C22 | semidirect |
| 23. #63371 | C22 | semidirect |
| 24. C2×C9⋊C16 | C22 | semidirect |
| 88. #576 | D9 | semidirect |
| 129. #135 | C2×D9 | semidirect |
| 131. C2×D8 | C2×D9 | semidirect |
| 191. C9 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#576 | 2 |
| #10589854 | 2 |
| #10588874 | 2 |
| #10588873 | 2 |
| #10588827 | 2 |
| C2×#63385 | 2 |
| #10588820 | 2 |
| #84007 | 3 |