Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27212364 | C2 | semidirect |
| 2. #27212361 | C2 | semidirect |
| 3. #27212359 | C2 | semidirect |
| 4. #27212355 | C2 | semidirect |
| 5. #27212352 | C2 | semidirect |
| 6. #27212352 | C2 | semidirect |
| 7. #27212351 | C2 | semidirect |
| 8. #27212349 | C2 | semidirect |
| 9. #27212344 | C2 | semidirect |
| 10. #27212344 | C2 | semidirect |
| 12. #27212331 | C2 | semidirect |
| 13. C4×C22⋊D421 | C2 | semidirect |
| 14. #27212324 | C2 | semidirect |
| 15. C22⋊Q8×C421 | C2 | semidirect |
| 103. C421 | #542 | semidirect |
| 115. C22⋊Q8 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212364 | 2 |
| #27212361 | 2 |
| #27212359 | 2 |
| #27212355 | 2 |
| #27212352 | 2 |
| #27212351 | 2 |
| #27212349 | 2 |
| #27212344 | 2 |
| #27212339 | 2 |
| #27212331 | 2 |
| C4×C22⋊D421 | 2 |
| #27212324 | 2 |
| C22⋊Q8×C421 | 2 |
| #542 | 421 |