Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 55 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×#20294080 | C2 | semidirect |
| 3. #28357178 | C2 | semidirect |
| 4. #28357142 | C2 | semidirect |
| 5. #28357141 | C2 | semidirect |
| 6. #28357140 | C2 | semidirect |
| 7. #102×C433 | C2 | semidirect |
| 12. D4×D433 | C4 | semidirect |
| 15. C2×#16812358 | C22 | semidirect |
| 16. C4⋊Dic433 | C22 | semidirect |
| 20. C2×C8×C433 | C22 | semidirect |
| 21. C4⋊C4×C433 | C22 | semidirect |
| 63. C433 | #418 | semidirect |
| 71. #102 | D433 | semidirect |
| 81. C2×C8 | C2×D433 | semidirect |
| 83. 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×#20294080 | 2 |
| #28357178 | 2 |
| #28357142 | 2 |
| #28357141 | 2 |
| #28357140 | 2 |
| #102×C433 | 2 |
| #418 | 433 |