Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27212361 | C2 | semidirect |
| 2. #27212357 | C2 | semidirect |
| 3. #27212355 | C2 | semidirect |
| 4. #27212350 | C2 | semidirect |
| 6. Q8×Dic421 | C2 | semidirect |
| 7. #27212328 | C2 | semidirect |
| 8. #27212326 | C2 | semidirect |
| 9. #27212324 | C2 | semidirect |
| 10. C2×C4×Dic421 | C2 | semidirect |
| 11. C22⋊Q8×C421 | C2 | semidirect |
| 74. C421 | #529 | semidirect |
| 80. C22⋊Q8 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212361 | 2 |
| #27212357 | 2 |
| #27212355 | 2 |
| #27212350 | 2 |
| #27212340 | 2 |
| Q8×Dic421 | 2 |
| #27212328 | 2 |
| #27212326 | 2 |
| #27212324 | 2 |
| C2×C4×Dic421 | 2 |
| C22⋊Q8×C421 | 2 |
| #529 | 421 |