Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×C4×Dic433 | C2 | semidirect |
| 4. #28357127 | C2 | semidirect |
| 5. C2×C42×C433 | C2 | semidirect |
| 11. C2×C4×D433 | C4 | semidirect |
| 12. #20294074 | C4 | direct (N × H) |
| 27. C2×Dic433 | C2×C4 | semidirect |
| 33. C2×C4×C433 | C2×C4 | semidirect |
| 45. C2×D433 | C42 | semidirect |
| 47. C4×C433 | C22⋊C4 | semidirect |
| 56. C433 | C4×C22⋊C4 | semidirect |
| 61. C2×C42 | D433 | semidirect |
| 90. C2×C4 | C4×D433 | semidirect |
| 106. C4 | #20294074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D433 | 2 |
| C2×#20294074 | 2 |
| C2×C4×Dic433 | 2 |
| #28357127 | 2 |
| C2×C42×C433 | 2 |
| C4×C22⋊C4 | 433 |