Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10589847 | C2 | semidirect |
| 3. #10588819 | C2 | semidirect |
| 4. #10588686 | C2 | semidirect |
| 5. #10588685 | C2 | semidirect |
| 6. C9×#339 | C2 | semidirect |
| 7. #10588201 | C2 | semidirect |
| 20. #63437 | C4 | semidirect |
| 21. #63437 | C4 | semidirect |
| 22. #63436 | C4 | semidirect |
| 24. #63431 | C4 | semidirect |
| 55. C9×M16 | D4 | semidirect |
| 70. #3667 | D4 | semidirect |
| 135. #339 | D9 | semidirect |
| 276. M16 | D36 | semidirect |
| 310. C9 | #1884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589847 | 2 |
| #10589579 | 2 |
| #10588819 | 2 |
| #10588686 | 2 |
| #10588685 | 2 |
| C9×#339 | 2 |
| #10588201 | 2 |
| #68777 | 3 |