Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
654 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 127 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. C24×C27⋊C3 | C2 | semidirect |
| 2. C2×#6171⋊C3 | C2 | semidirect |
| 3. #88372⋊C3 | C2 | semidirect |
| 5. #11720202 | C3 | semidirect |
| 8. C22×D27⋊C3 | C22 | semidirect |
| 10. C2×(C27⋊C3)⋊C4 | C22 | semidirect |
| 14. C24×C27 | C2×C3 | semidirect |
| 16. C2×#6171 | C2×C3 | semidirect |
| 17. #88372 | C2×C3 | semidirect |
| 20. C22×C27⋊C3 | D4 | semidirect |
| 35. C22×D27 | C22×C3 | semidirect |
| 37. C2×Dic27 | C22×C3 | semidirect |
| 60. C22×C27 | C3×D4 | semidirect |
| 66. C27⋊C3 | #120 | semidirect |
| 112. C27 | C3×#120 | semidirect |
| 131. C24 | D27⋊C3 | semidirect |
| 163. C22 | #6171⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C27⋊C3 | 2 |
| C2×#6171⋊C3 | 2 |
| #88372⋊C3 | 2 |
| C3×#63515 | 3 |
| #11720202 | 3 |