Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
241 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 76 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×Dic24 | C2 | semidirect |
| 3. C2×C3⋊(C3⋊C32) | C2 | semidirect |
| 4. #10589072 | C2 | direct (N × H) |
| 11. C3×Dic24 | C22 | semidirect |
| 14. C3⋊(C3⋊C32) | C22 | semidirect |
| 17. C2×Dic24 | D3 | semidirect |
| 46. Dic24 | C2×D3 | semidirect |
| 121. C2×C32 | SD64 | semidirect |
| 148. C32 | C2×SD64 | semidirect |
| 161. C2×C3 | #4520 | semidirect |
| 162. C2×C3 | #4521 | semidirect |
| 173. C3 | C2×#4520 | semidirect |
| 174. C3 | C2×#4521 | semidirect |
| 176. C2 | #10589072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| C2×C3×D48 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| #10589072 | 2 |
| C2×#4521 | 3 |
| C2×#4520 | 3 |