Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1002 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 214 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. C2×C9×#127 | C2 | semidirect |
| 2. C22×#3673 | C2 | semidirect |
| 3. C22×#3672 | C2 | semidirect |
| 4. C2×#63437 | C2 | semidirect |
| 5. #10588756 | C2 | direct (N × H) |
| 6. C2×#63362 | C2 | semidirect |
| 13. C9×#127 | C22 | semidirect |
| 16. C2×#3673 | C22 | semidirect |
| 18. C2×#3672 | C22 | semidirect |
| 22. #63437 | C22 | semidirect |
| 23. #63362 | C22 | semidirect |
| 52. C2×C9⋊C8 | D4 | semidirect |
| 93. C9⋊C8 | C2×D4 | semidirect |
| 96. C2×#127 | D9 | semidirect |
| 147. #127 | C2×D9 | semidirect |
| 177. C2×C9 | #496 | semidirect |
| 218. C9 | C2×#496 | semidirect |
| 263. C2 | #10588756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#127 | 2 |
| C22×#3673 | 2 |
| C22×#3672 | 2 |
| C2×#63437 | 2 |
| #10588756 | 2 |
| C2×#63362 | 2 |
| C2×#5074 | 3 |