Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
559 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×#88691 | C2 | semidirect |
| 2. C3⋊#88691 | C2 | semidirect |
| 5. C3⋊#63700 | C3 | semidirect |
| 7. C3×#6204 | C22 | semidirect |
| 16. #88691 | D3 | semidirect |
| 17. C3×#41⋊C9 | C2×C3 | semidirect |
| 18. C3⋊(#41⋊C9) | C2×C3 | semidirect |
| 38. #6204 | C2×D3 | semidirect |
| 39. C3×Q8⋊C9 | C22×C3 | semidirect |
| 60. #41⋊C9 | C3×D3 | semidirect |
| 75. #1009 | 3−1+2 | semidirect |
| 112. Q8⋊C9 | C2×C3×D3 | semidirect |
| 285. C3 | #11722576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#88691 | 2 |
| C3⋊#88691 | 2 |
| C32×#1009 | 3 |
| #11722576 | 3 |
| C3⋊#63700 | 3 |
| Dic6×3−1+2 | 4 |