Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×#20294105 | C2 | semidirect |
| 2. C2×C4⋊#13181884 | C2 | semidirect |
| 3. #28357282 | C2 | direct (N × H) |
| 7. #20294105 | C22 | semidirect |
| 10. C4⋊#13181884 | C22 | semidirect |
| 12. C2×D1732 | C4 | semidirect |
| 16. D4×D433 | C4 | semidirect |
| 19. C2×D4×C433 | C4 | semidirect |
| 30. D1732 | C2×C4 | semidirect |
| 40. D4×C433 | C2×C4 | semidirect |
| 60. C2×C433 | #102 | semidirect |
| 63. D433 | #102 | semidirect |
| 66. C433 | C2×#102 | semidirect |
| 79. C2×D4 | #13181884 | semidirect |
| 99. D4 | C2×#13181884 | semidirect |
| 131. C2 | #28357282 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294105 | 2 |
| C2×C4⋊#13181884 | 2 |
| #28357282 | 2 |
| C2×D4×D433 | 2 |
| C2×#102 | 433 |