Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #27212399 | C2 | semidirect |
| 3. C2×#20269760 | C2 | semidirect |
| 4. #27212372 | C2 | semidirect |
| 5. #27212284 | C2 | semidirect |
| 6. #27212282 | C2 | semidirect |
| 7. #108×C421 | C2 | semidirect |
| 51. C421 | #471 | semidirect |
| 57. #108 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212399 | 2 |
| #27212394 | 2 |
| C2×#20269760 | 2 |
| #27212372 | 2 |
| #27212284 | 2 |
| #27212282 | 2 |
| #108×C421 | 2 |
| #471 | 421 |