Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #10592594 | C2 | semidirect |
| 3. C32×#368 | C2 | semidirect |
| 4. C16×C3⋊Dic3 | C2 | semidirect |
| 5. #10589363 | C2 | semidirect |
| 14. #63628 | C4 | semidirect |
| 15. #63627 | C4 | semidirect |
| 16. #63626 | C4 | semidirect |
| 19. C3×#368 | D3 | semidirect |
| 59. #368 | C3⋊D3 | semidirect |
| 124. C32 | #2178 | semidirect |
| 145. C3 | #69357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592603 | 2 |
| #10592594 | 2 |
| C32×#368 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589363 | 2 |
| #69357 | 3 |