Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 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. #27212364 | C2 | semidirect |
| 3. #27212355 | C2 | semidirect |
| 4. #27212349 | C2 | semidirect |
| 5. #27212342 | C2 | semidirect |
| 6. #27212325 | C2 | semidirect |
| 7. C22×Q8×C421 | C2 | semidirect |
| 52. C421 | #536 | semidirect |
| 55. C22×Q8 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269771 | 2 |
| #27212364 | 2 |
| #27212355 | 2 |
| #27212349 | 2 |
| #27212342 | 2 |
| #27212325 | 2 |
| C22×Q8×C421 | 2 |
| #536 | 421 |