Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
897 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 897 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C22⋊C4×D9 | C2 | semidirect |
| 3. C2×C9×#99 | C2 | semidirect |
| 4. C2×#63393 | C2 | semidirect |
| 5. #10588635 | C2 | semidirect |
| 6. #10588204 | C2 | semidirect |
| 7. #10588204 | C2 | semidirect |
| 11. C22×#611 | C4 | semidirect |
| 23. C2×(C2×D9)⋊C4 | C4 | semidirect |
| 35. C24×C9 | C2×C4 | semidirect |
| 54. C22×C4×C9 | C2×C4 | semidirect |
| 60. C22×Dic9 | C2×C4 | semidirect |
| 66. C9×C22⋊C4 | D4 | semidirect |
| 72. #3676 | D4 | semidirect |
| 152. C2×#99 | D9 | semidirect |
| 229. C2×D9 | #99 | semidirect |
| 327. C24 | C4×D9 | semidirect |
| 345. C22×C4 | C4×D9 | semidirect |
| 359. C22⋊C4 | #611 | semidirect |
| 398. C9 | #1898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63499 | 2 |
| C2×C22⋊C4×D9 | 2 |
| C2×C9×#99 | 2 |
| C2×#63393 | 2 |
| #10588635 | 2 |
| #10588204 | 2 |
| #70036 | 3 |