Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1193 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1193 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 |
|---|---|---|
| 3. C2×C3×#817 | C2 | semidirect |
| 4. C2×#63576 | C2 | semidirect |
| 5. #10590712 | C2 | direct (N × H) |
| 10. C2×C8×C3⋊D3 | C4 | semidirect |
| 17. C3×#817 | C22 | semidirect |
| 18. #63576 | C22 | semidirect |
| 23. C2×#817 | D3 | semidirect |
| 38. C8×C3⋊D3 | C2×C4 | semidirect |
| 61. #817 | C2×D3 | semidirect |
| 174. C2×C32 | #427 | semidirect |
| 217. C32 | C2×#427 | semidirect |
| 238. C2×C3 | #4860 | semidirect |
| 255. C3 | C2×#4860 | semidirect |
| 257. C2 | #10590712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C2×#63849 | 2 |
| C2×C3×#817 | 2 |
| C2×#63576 | 2 |
| #10590712 | 2 |
| C2×#4860 | 3 |