Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
379 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 379 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 |
|---|---|---|
| 1. Q16×C3⋊Dic3 | C2 | semidirect |
| 4. C3×#4564 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 7. #10589102 | C2 | semidirect |
| 17. C3×#828 | C4 | semidirect |
| 30. #4564 | D3 | semidirect |
| 41. C32×Q16 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 73. #828 | Dic3 | semidirect |
| 117. C3×Q16 | C4×D3 | semidirect |
| 118. C3×Q16 | C2×Dic3 | semidirect |
| 148. C3⋊C16 | C2×Dic3 | semidirect |
| 158. C3⋊Dic3 | SD32 | semidirect |
| 220. Q16 | D3×Dic3 | semidirect |
| 262. C32 | C4×SD32 | semidirect |
| 301. C3 | #69206 | semidirect |
| 302. C3 | Dic3×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C3⋊Dic3 | 2 |
| C2×C3×#828 | 2 |
| #10590777 | 2 |
| C3×#4564 | 2 |
| #10589141 | 2 |
| #10589115 | 2 |
| #10589102 | 2 |
| Dic3×SD32 | 3 |
| #69206 | 3 |