Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
477 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 477 conjugacy classes of subgroups — too many to draw. Only its 132 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. #10592379 | C2 | semidirect |
| 4. #10590303 | C2 | semidirect |
| 5. C3×C8×C3⋊C8 | C2 | semidirect |
| 27. C8×C3⋊C8 | D3 | semidirect |
| 71. C32×C8 | SD16 | semidirect |
| 72. C3×C3⋊C8 | SD16 | semidirect |
| 147. C3×C8 | #204 | semidirect |
| 148. C3×C8 | #214 | semidirect |
| 149. C3⋊C8 | #204 | semidirect |
| 183. C32 | #1705 | semidirect |
| 194. C8 | #3716 | semidirect |
| 211. C3 | #68057 | semidirect |
| 212. C3 | #71254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592379 | 2 |
| C3×#4693 | 2 |
| #10590369 | 2 |
| #10590303 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #71254 | 3 |
| #68057 | 3 |