Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
190 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
| 4. C2×C4×#13181884 | C2 | semidirect |
| 5. (C2×#13181884)⋊C4 | C2 | semidirect |
| 6. (C2×#13181884)⋊C4 | C2 | semidirect |
| 19. C22⋊Dic433 | C4 | semidirect |
| 20. #20294074 | C4 | semidirect |
| 21. #20294074 | C4 | semidirect |
| 22. C22⋊C4×C433 | C4 | semidirect |
| 86. C433 | #388 | semidirect |
| 108. C22⋊C4 | #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×C4×#13181884 | 2 |
| (C2×#13181884)⋊C4 | 2 |
| C22⋊C4×D433 | 2 |
| #388 | 433 |