Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 5. #10592698 | C2 | semidirect |
| 6. #10589418 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 16. C32×#103 | C4 | semidirect |
| 17. C32×#102 | C4 | semidirect |
| 64. C3×#103 | Dic3 | semidirect |
| 65. C3×#102 | Dic3 | semidirect |
| 150. #103 | C3⋊Dic3 | semidirect |
| 151. #102 | C3⋊Dic3 | semidirect |
| 223. C32 | #1937 | semidirect |
| 266. C3 | #70287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#416 | 2 |
| C2×#63664 | 2 |
| #10592933 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| #10592698 | 2 |
| #10589418 | 2 |
| #10589398 | 2 |
| #70287 | 3 |