Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1200 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 297 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. C22×C32×D8 | C2 | semidirect |
| 2. C2×#64113 | C2 | semidirect |
| 3. C2×#63654 | C2 | semidirect |
| 4. #10592846 | C2 | direct (N × H) |
| 5. C2×#63653 | C2 | semidirect |
| 6. C2×#63639 | C2 | semidirect |
| 13. C2×C32×D8 | C22 | semidirect |
| 15. C2×#3746 | C22 | semidirect |
| 17. #64113 | C22 | semidirect |
| 18. C2×#3745 | C22 | semidirect |
| 20. #63654 | C22 | semidirect |
| 21. #63653 | C22 | semidirect |
| 22. #63639 | C22 | semidirect |
| 23. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 24. C22×C3×D8 | D3 | semidirect |
| 50. #3746 | C23 | semidirect |
| 52. #3745 | C23 | semidirect |
| 54. C3⋊(C3⋊C16) | C23 | semidirect |
| 61. C2×C3×D8 | C2×D3 | semidirect |
| 95. C22×D8 | C3⋊D3 | semidirect |
| 147. C2×D8 | C2×C3⋊D3 | semidirect |
| 177. C2×C32 | #509 | semidirect |
| 217. C32 | C2×#509 | semidirect |
| 242. C2×C3 | #5147 | semidirect |
| 257. C3 | C2×#5147 | semidirect |
| 261. C2 | #10592846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×#64113 | 2 |
| C2×#63654 | 2 |
| #10592846 | 2 |
| C2×#63653 | 2 |
| C2×#63639 | 2 |
| C2×#5147 | 3 |