Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
361 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 361 conjugacy classes of subgroups — too many to draw. Only its 102 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×#798 | C2 | semidirect |
| 3. C2×#63542 | C2 | semidirect |
| 4. #10589373 | C2 | semidirect |
| 5. C3×Dic3⋊C16 | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 25. C2×#798 | D3 | semidirect |
| 36. Dic3⋊C16 | D3 | semidirect |
| 56. C3×C3⋊C16 | D4 | semidirect |
| 155. C3⋊C16 | #67 | semidirect |
| 159. C2×C3⋊D3 | M32 | semidirect |
| 281. C32 | #2168 | semidirect |
| 327. C3 | #69278 | semidirect |
| 328. C3 | #71433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#798 | 2 |
| C8×#626 | 2 |
| C2×#63542 | 2 |
| #10589373 | 2 |
| C3×Dic3⋊C16 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #10589103 | 2 |
| #71433 | 3 |
| #69278 | 3 |