Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
768 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 161 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×#63654 | C2 | semidirect |
| 3. #10592815 | C2 | semidirect |
| 4. #10589428 | C2 | semidirect |
| 5. #10589415 | C2 | semidirect |
| 13. C2×#3746 | C22 | semidirect |
| 15. #63645 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 100. C22×C32 | SD32 | semidirect |
| 165. C22×C3 | #827 | semidirect |
| 172. C32 | #2187 | semidirect |
| 202. C22 | #63654 | semidirect |
| 209. C3 | #72036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×#63654 | 2 |
| #10592815 | 2 |
| #10589428 | 2 |
| #10589415 | 2 |
| #72036 | 3 |