Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
250 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 68 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×C3×Dic24 | C2 | semidirect |
| 3. C3×#4499 | C2 | semidirect |
| 4. #10589076 | C2 | semidirect |
| 5. #10589074 | C2 | semidirect |
| 18. C2×Dic24 | D3 | semidirect |
| 25. #4499 | D3 | semidirect |
| 176. C32 | #2264 | semidirect |
| 203. C3 | #69374 | semidirect |
| 204. C3 | #71493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592603 | 2 |
| C2×C3×Dic24 | 2 |
| C3×#4499 | 2 |
| #10589076 | 2 |
| #10589074 | 2 |
| #71493 | 3 |
| #69374 | 3 |