Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #10682994 | C2 | semidirect |
| 2. #10682870 | C2 | semidirect |
| 17. C3×Q64 | C8 | semidirect |
| 19. C3×D32 | C8 | semidirect |
| 50. Q64 | C3⋊C8 | semidirect |
| 52. D32 | C3⋊C8 | semidirect |
| 139. C3 | #94613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10682994 | 2 |
| #10682870 | 2 |
| C3×#13656 | 2 |
| #94613 | 3 |