Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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×#20294086 | C2 | semidirect |
| 3. C2×#20294085 | C2 | semidirect |
| 4. #28357200 | C2 | semidirect |
| 5. #28357140 | C2 | semidirect |
| 6. #28357132 | C2 | semidirect |
| 7. #102×C433 | C2 | semidirect |
| 9. C2×Dic866 | C22 | semidirect |
| 17. C2×#16812358 | C22 | semidirect |
| 21. C2×C8×C433 | C22 | semidirect |
| 22. C4⋊C4×C433 | C22 | semidirect |
| 54. C2×D433 | SD16 | semidirect |
| 66. C433 | #450 | semidirect |
| 73. #102 | D433 | semidirect |
| 86. C2×C8 | C2×D433 | semidirect |
| 88. C4⋊C4 | C2×D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D433 | 2 |
| C2×#20294086 | 2 |
| C2×#20294085 | 2 |
| #28357200 | 2 |
| #28357140 | 2 |
| #28357132 | 2 |
| #102×C433 | 2 |
| #450 | 433 |