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. #27212359 | C2 | semidirect |
| 3. #27212356 | C2 | semidirect |
| 4. #27212352 | C2 | semidirect |
| 5. #27212350 | C2 | semidirect |
| 6. #27212347 | C2 | semidirect |
| 7. #27212343 | C2 | semidirect |
| 9. C4×Dic842 | C2 | semidirect |
| 10. C4×C22⋊D421 | C2 | semidirect |
| 11. C4×C22⋊D421 | C2 | semidirect |
| 12. #27212325 | C2 | semidirect |
| 13. #27212323 | C2 | semidirect |
| 14. C2×C4×Dic421 | C2 | semidirect |
| 15. C4×D4×C421 | C2 | semidirect |
| 103. C421 | #529 | semidirect |
| 116. C4×D4 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212361 | 2 |
| #27212359 | 2 |
| #27212356 | 2 |
| #27212352 | 2 |
| #27212350 | 2 |
| #27212347 | 2 |
| #27212343 | 2 |
| #27212338 | 2 |
| C4×Dic842 | 2 |
| C4×C22⋊D421 | 2 |
| #27212325 | 2 |
| #27212323 | 2 |
| C2×C4×Dic421 | 2 |
| C4×D4×C421 | 2 |
| #529 | 421 |