Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #27212356 | C2 | semidirect |
| 3. #27212356 | C2 | semidirect |
| 4. #27212344 | C2 | semidirect |
| 5. #27212344 | C2 | semidirect |
| 6. #27212343 | C2 | semidirect |
| 7. #27212343 | C2 | semidirect |
| 8. #27212342 | C2 | semidirect |
| 9. #27212331 | C2 | semidirect |
| 13. C2×#20269750 | C2 | semidirect |
| 14. C4⋊C4×D421 | C2 | semidirect |
| 15. C22⋊Q8×C421 | C2 | semidirect |
| 54. C22⋊D421 | Q8 | semidirect |
| 101. C421 | #554 | semidirect |
| 111. 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 |
| #27212356 | 2 |
| #27212344 | 2 |
| #27212343 | 2 |
| #27212342 | 2 |
| #27212331 | 2 |
| C4×C22⋊D421 | 2 |
| #27212326 | 2 |
| C2×#20269750 | 2 |
| C4⋊C4×D421 | 2 |
| C22⋊Q8×C421 | 2 |
| #554 | 421 |