Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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. #27212374 | C2 | semidirect |
| 3. #27212373 | C2 | semidirect |
| 4. #27212301 | C2 | semidirect |
| 5. #27212294 | C2 | semidirect |
| 6. #27212277 | C2 | semidirect |
| 7. #104×C421 | C2 | semidirect |
| 9. #20269761 | C4 | semidirect |
| 10. #20269759 | C4 | semidirect |
| 11. #20269758 | C4 | semidirect |
| 12. #20269756 | C4 | semidirect |
| 51. C421 | #444 | semidirect |
| 58. #104 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212386 | 2 |
| #27212374 | 2 |
| #27212373 | 2 |
| #27212301 | 2 |
| #27212294 | 2 |
| #27212277 | 2 |
| #104×C421 | 2 |
| #444 | 421 |