Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
519 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 519 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 |
|---|---|---|
| 2. #10589623 | C2 | semidirect |
| 3. C9×#410 | C2 | semidirect |
| 4. #10588914 | C2 | semidirect |
| 5. #10588682 | C2 | semidirect |
| 6. #10588210 | C2 | semidirect |
| 7. #10588209 | C2 | semidirect |
| 15. C2×#3675 | C4 | semidirect |
| 16. C2×#3673 | C4 | semidirect |
| 38. C2×Q8×C9 | C2×C4 | semidirect |
| 40. C2×D4×C9 | C2×C4 | semidirect |
| 67. C2×C9⋊C8 | C2×C4 | semidirect |
| 121. #410 | D9 | semidirect |
| 236. C2×Q8 | C4×D9 | semidirect |
| 244. C2×D4 | C4×D9 | semidirect |
| 284. C9 | #1904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63512 | 2 |
| #10589623 | 2 |
| C9×#410 | 2 |
| #10588914 | 2 |
| #10588682 | 2 |
| #10588210 | 2 |
| #10588209 | 2 |
| #70049 | 3 |