Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
353 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C4×Dic12 | C2 | semidirect |
| 4. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 5. #10589142 | C2 | semidirect |
| 6. #10589117 | C2 | semidirect |
| 21. #63547 | C4 | direct (N × H) |
| 26. C4×Dic12 | D3 | semidirect |
| 49. C3×Dic12 | C2×C4 | semidirect |
| 53. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 134. Dic12 | C4×D3 | semidirect |
| 148. C32×C4 | SD32 | semidirect |
| 241. C3×C4 | #827 | semidirect |
| 242. C3×C4 | #828 | semidirect |
| 250. C32 | C4×SD32 | semidirect |
| 285. C4 | #63547 | direct (N × H) |
| 289. C3 | C4×#827 | semidirect |
| 290. C3 | C4×#828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic12 | 2 |
| C3×C4×D24 | 2 |
| C2×#63547 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #10589142 | 2 |
| #10589117 | 2 |
| #10589114 | 2 |
| C4×#828 | 3 |
| C4×#827 | 3 |