Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 171 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. #10592823 | C2 | semidirect |
| 5. M16×C3⋊Dic3 | C2 | semidirect |
| 6. #10589399 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 19. #63663 | C4 | semidirect |
| 20. #63660 | C4 | semidirect |
| 236. C32 | #1932 | semidirect |
| 281. C3 | #70401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#421 | 2 |
| #10592936 | 2 |
| C2×#63664 | 2 |
| #10592823 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10589399 | 2 |
| #10589398 | 2 |
| #70401 | 3 |