Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
2452 conjugacy classes of subgroups; only the 461 normal subgroups are shown.
This group has 2452 conjugacy classes of subgroups — too many to draw. Only its 461 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. #10803643 | C2 | semidirect |
| 2. #10695026 | C2 | semidirect |
| 3. #10688954 | C2 | semidirect |
| 4. #10684562 | C2 | semidirect |
| 10. C3×#1712 | C4 | semidirect |
| 26. C3×#493 | C2×C4 | semidirect |
| 36. C3×C82 | C2×C4 | semidirect |
| 45. #1712 | Dic3 | semidirect |
| 72. #493 | C2×Dic3 | semidirect |
| 83. C82 | C2×Dic3 | semidirect |
| 135. C3×C8 | #442 | semidirect |
| 178. C8 | #5152 | semidirect |
| 191. C3 | #212918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10803643 | 2 |
| #10695026 | 2 |
| #10688954 | 2 |
| #10684562 | 2 |
| C2×C3×#1712 | 2 |
| #212918 | 3 |