Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
628 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 79 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. #13049465 | C2 | semidirect |
| 4. C3×#88946 | C2 | semidirect |
| 11. C3⋊D3×#157 | C4 | semidirect |
| 15. #88946 | D3 | semidirect |
| 23. C3⋊(C3⋊#157) | C2×C4 | semidirect |
| 25. C32×#157 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊(C3⋊D3)) | C4⋊C4 | semidirect |
| 42. C32×C3⋊D3 | C4⋊C4 | semidirect |
| 75. C3×#157 | C4×D3 | semidirect |
| 77. C34 | C2×C4⋊C4 | semidirect |
| 145. #157 | #624 | semidirect |
| 154. C33 | D3×C4⋊C4 | semidirect |
| 190. C3⋊D3 | #3777 | semidirect |
| 234. C32 | #63900 | semidirect |
| 235. C32 | C2×#3777 | semidirect |
| 273. C3 | D3×#3777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620197 | 2 |
| C2×C3⋊D3×#157 | 2 |
| #13049465 | 2 |
| C3×#88946 | 2 |
| D3×#3777 | 3 |
| #63900 | 9 |