Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
234 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 70 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×C4⋊#13181884 | C2 | semidirect |
| 3. (C2×#13181884)⋊C4 | C2 | semidirect |
| 9. C22×Dic433 | C4 | semidirect |
| 11. C2×C4×D433 | C4 | semidirect |
| 12. C2×C4×D433 | C4 | semidirect |
| 15. C22×C4×C433 | C4 | semidirect |
| 38. C22×C433 | C4⋊C4 | semidirect |
| 44. C2×D433 | C4⋊C4 | semidirect |
| 51. C4×C433 | C22⋊C4 | semidirect |
| 53. Dic433 | C22⋊C4 | semidirect |
| 61. C433 | #380 | semidirect |
| 75. C22×C4 | #13181884 | semidirect |
| 109. C22 | C4⋊#13181884 | semidirect |
| 115. C4 | C22⋊#13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13181884 | 2 |
| C2×C22⋊#13181884 | 2 |
| (C2×#13181884)⋊C4 | 2 |
| C22×C4×D433 | 2 |
| #380 | 433 |