Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
128 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 41 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×#20294086 | C2 | semidirect |
| 2. C2×#20294085 | C2 | semidirect |
| 4. #28357185 | C2 | semidirect |
| 5. #28357149 | C2 | semidirect |
| 6. #28357140 | C2 | semidirect |
| 7. #102×C433 | C2 | semidirect |
| 23. Dic866 | D4 | semidirect |
| 50. Dic433 | SD16 | semidirect |
| 56. C433 | #460 | semidirect |
| 64. #102 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294086 | 2 |
| C2×#20294085 | 2 |
| #28357216 | 2 |
| #28357185 | 2 |
| #28357149 | 2 |
| #28357140 | 2 |
| #102×C433 | 2 |
| #460 | 433 |