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 |
|---|---|---|
| 2. C2×#64145 | C2 | semidirect |
| 3. C22×#3754 | C2 | semidirect |
| 4. C22×#3746 | C2 | semidirect |
| 5. #10592854 | C2 | direct (N × H) |
| 6. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 15. #64145 | C22 | semidirect |
| 17. C2×#3754 | C22 | semidirect |
| 21. C2×#3746 | C22 | semidirect |
| 22. C8×C3⋊Dic3 | C22 | semidirect |
| 162. C2×C32 | #495 | semidirect |
| 198. C32 | C2×#495 | semidirect |
| 220. C2×C3 | #5155 | semidirect |
| 234. C3 | C2×#5155 | semidirect |
| 236. C2 | #10592854 | 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×#64145 | 2 |
| C22×#3754 | 2 |
| C22×#3746 | 2 |
| #10592854 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×#5155 | 3 |