Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 4. C3×#4489 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 16. #63544 | C4 | semidirect |
| 24. #4489 | D3 | semidirect |
| 37. C3×C3⋊C16 | C2×C4 | semidirect |
| 96. C3⋊C16 | C4×D3 | semidirect |
| 177. C32 | #2159 | semidirect |
| 209. C3 | #69326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592579 | 2 |
| #10590687 | 2 |
| C2×#63544 | 2 |
| C3×#4489 | 2 |
| #10589141 | 2 |
| #69326 | 3 |