Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1776 conjugacy classes of subgroups; only the 361 normal subgroups are shown.
This group has 1776 conjugacy classes of subgroups — too many to draw. Only its 361 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×Q16 | C2 | semidirect |
| 2. C2×#64156 | C2 | semidirect |
| 3. C22×#3755 | C2 | semidirect |
| 5. #10592890 | C2 | direct (N × H) |
| 6. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 11. C2×C32×Q16 | C22 | semidirect |
| 14. #64156 | C22 | semidirect |
| 16. C2×#3755 | C22 | semidirect |
| 22. C8×C3⋊Dic3 | C22 | semidirect |
| 23. C22×C3×Q16 | D3 | semidirect |
| 55. C2×C3×Q16 | C2×D3 | semidirect |
| 87. C22×Q16 | C3⋊D3 | semidirect |
| 129. C2×Q16 | C2×C3⋊D3 | semidirect |
| 161. C2×C32 | #495 | semidirect |
| 198. C32 | C2×#495 | semidirect |
| 219. C2×C3 | #5191 | semidirect |
| 234. C3 | C2×#5191 | semidirect |
| 236. C2 | #10592890 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C2×#64156 | 2 |
| C22×#3755 | 2 |
| C22×#3745 | 2 |
| #10592890 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×#5191 | 3 |