Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 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×C22⋊#13181884 | C2 | semidirect |
| 2. #28357279 | C2 | direct (N × H) |
| 6. C22⋊#13181884 | C22 | semidirect |
| 7. C23×D433 | C4 | semidirect |
| 11. C2×D1732 | C4 | semidirect |
| 13. C22×C4×C433 | C4 | semidirect |
| 21. C22×D433 | C2×C4 | semidirect |
| 30. C2×C4×C433 | C2×C4 | semidirect |
| 49. C2×C433 | #99 | semidirect |
| 54. C433 | C2×#99 | semidirect |
| 66. C22×C4 | #13181884 | semidirect |
| 85. C2×C4 | C2×#13181884 | semidirect |
| 107. C2 | #28357279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13181884 | 2 |
| #28357279 | 2 |
| C22×D1732 | 2 |
| C2×#99 | 433 |