Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1020 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 229 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×C32×C22⋊C8 | C2 | semidirect |
| 3. #10592911 | C2 | semidirect |
| 4. #10589336 | C2 | semidirect |
| 8. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 13. #64139 | C4 | semidirect |
| 17. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 19. C32×C22⋊C8 | C22 | semidirect |
| 20. #63658 | C22 | semidirect |
| 22. C2×C3×C22⋊C8 | D3 | semidirect |
| 65. C3×C22⋊C8 | C2×D3 | semidirect |
| 100. C2×C22⋊C8 | C3⋊D3 | semidirect |
| 165. C22⋊C8 | C2×C3⋊D3 | semidirect |
| 256. C32 | #1519 | semidirect |
| 320. C3 | #69944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64139 | 2 |
| C2×C32×C22⋊C8 | 2 |
| #10592911 | 2 |
| #10589336 | 2 |
| #69944 | 3 |