Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
1090 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 220 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 |
| 4. #11722576 | C3 | direct (N × H) |
| 5. C3×#63700 | C3 | semidirect |
| 7. C3×#6204 | C22 | semidirect |
| 13. #88691 | C2×C3 | semidirect |
| 14. #88691 | C2×C3 | semidirect |
| 15. C3×#41⋊C9 | C2×C3 | semidirect |
| 16. C3×#41⋊C9 | C2×C3 | semidirect |
| 22. #63700 | C32 | semidirect |
| 34. #6204 | C22×C3 | semidirect |
| 35. C3×Q8⋊C9 | C22×C3 | semidirect |
| 55. #41⋊C9 | C2×C32 | semidirect |
| 56. #41⋊C9 | C2×C32 | semidirect |
| 68. C3×H(5,𝔽2) | 3−1+2 | semidirect |
| 106. Q8⋊C9 | C22×C32 | semidirect |
| 154. H(5,𝔽2) | C3×3−1+2 | semidirect |
| 262. C3 | #11722576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#88691 | 2 |
| C33×H(5,𝔽2) | 3 |
| #11722576 | 3 |
| C3×#63700 | 3 |
| C3×Q8×3−1+2 | 4 |