Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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×#20294084 | C2 | semidirect |
| 3. #28357196 | C2 | semidirect |
| 4. #28357144 | C2 | semidirect |
| 5. #28357142 | C2 | semidirect |
| 6. #28357132 | C2 | semidirect |
| 7. C2×Q16×C433 | C2 | semidirect |
| 60. C433 | #452 | semidirect |
| 63. C2×Q16 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294098 | 2 |
| C2×#20294084 | 2 |
| #28357196 | 2 |
| #28357144 | 2 |
| #28357142 | 2 |
| #28357132 | 2 |
| C2×Q16×C433 | 2 |
| #452 | 433 |