Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1601 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1601 conjugacy classes of subgroups — too many to draw. Only its 316 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×C3×#874 | C2 | semidirect |
| 2. C22×#3713 | C2 | semidirect |
| 3. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #10590352 | C2 | direct (N × H) |
| 11. C3×#874 | C22 | semidirect |
| 13. C2×#3713 | C22 | semidirect |
| 14. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 17. C2×#874 | D3 | semidirect |
| 31. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 48. #874 | C2×D3 | semidirect |
| 55. C2×C32×C4 | D8 | semidirect |
| 63. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 100. C32×C4 | C2×D8 | semidirect |
| 127. C2×C3×C4 | #213 | semidirect |
| 137. C2×C32 | #493 | semidirect |
| 169. C3×C4 | C2×#213 | semidirect |
| 172. C32 | C2×#493 | semidirect |
| 180. C2×C4 | #3713 | semidirect |
| 190. C2×C3 | #5073 | semidirect |
| 200. C4 | C2×#3713 | semidirect |
| 204. C3 | C2×#5073 | semidirect |
| 206. C2 | #10590352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#874 | 2 |
| C22×#3713 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10590352 | 2 |
| C2×#5073 | 3 |