Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10589921 | C2 | semidirect |
| 3. C9×#410 | C2 | semidirect |
| 4. #10588685 | C2 | semidirect |
| 5. #10588208 | C2 | semidirect |
| 11. #63509 | C4 | semidirect |
| 12. #63506 | C4 | semidirect |
| 13. #63502 | C4 | semidirect |
| 15. #63498 | C4 | semidirect |
| 53. #3667 | D4 | semidirect |
| 100. #410 | D9 | semidirect |
| 235. C9 | #1884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589934 | 2 |
| #10589921 | 2 |
| C9×#410 | 2 |
| #10588685 | 2 |
| #10588208 | 2 |
| #70045 | 3 |