Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 3. #10592823 | C2 | semidirect |
| 4. M16×C3⋊Dic3 | C2 | semidirect |
| 6. C32×#344 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 18. #63651 | C4 | semidirect |
| 19. #63650 | C4 | semidirect |
| 29. C3×#344 | D3 | semidirect |
| 105. #344 | C3⋊D3 | semidirect |
| 236. C32 | #1932 | semidirect |
| 281. C3 | #69012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63652 | 2 |
| #10592831 | 2 |
| #10592823 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10592704 | 2 |
| C32×#344 | 2 |
| #10589398 | 2 |
| #69012 | 3 |