Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
234 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. C2×#20294076 | C2 | semidirect |
| 4. #28357127 | C2 | semidirect |
| 5. #95×C433 | C2 | semidirect |
| 10. C2×C4×D433 | C4 | semidirect |
| 41. C2×D433 | C4⋊C4 | semidirect |
| 45. Dic433 | C22⋊C4 | semidirect |
| 52. C433 | #380 | semidirect |
| 58. #95 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D433 | 2 |
| C2×#20294076 | 2 |
| C2×#20294074 | 2 |
| #28357127 | 2 |
| #95×C433 | 2 |
| #380 | 433 |