Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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. C22×C3×C27⋊C3 | C2 | semidirect |
| 2. C2×C3⋊(D27⋊C3) | C2 | semidirect |
| 3. C3⋊((C27⋊C3)⋊C4) | C2 | semidirect |
| 5. #10619677 | C3 | semidirect |
| 14. C22×C27⋊C3 | D3 | semidirect |
| 16. C22×C3×C27 | C2×C3 | semidirect |
| 17. C2×C3⋊D27 | C2×C3 | semidirect |
| 19. C3⋊Dic27 | C2×C3 | semidirect |
| 21. C3×C27⋊C3 | D4 | semidirect |
| 56. C22×C27 | C3×D3 | semidirect |
| 61. C27⋊C3 | #67 | semidirect |
| 63. C3×C27 | C3×D4 | semidirect |
| 118. C27 | C3×#67 | semidirect |
| 146. C22×C3 | D27⋊C3 | semidirect |
| 174. C22 | C3⋊(D27⋊C3) | semidirect |
| 178. C3 | #6171⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C27⋊C3 | 2 |
| C2×C3⋊(D27⋊C3) | 2 |
| C3⋊((C27⋊C3)⋊C4) | 2 |
| C3×#6233 | 3 |
| #10619677 | 3 |
| #6171⋊C3 | 3 |