Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D421 | C2 | semidirect |
| 3. #27212365 | C2 | semidirect |
| 4. #27212352 | C2 | semidirect |
| 5. #27212351 | C2 | semidirect |
| 6. #27212348 | C2 | semidirect |
| 7. #27212346 | C2 | semidirect |
| 8. #27212345 | C2 | semidirect |
| 9. #27212342 | C2 | semidirect |
| 10. #27212324 | C2 | semidirect |
| 11. C22⋊Q8×C421 | C2 | semidirect |
| 83. C421 | #536 | semidirect |
| 94. 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 |
| C2×Q8×D421 | 2 |
| #27212365 | 2 |
| #27212352 | 2 |
| #27212351 | 2 |
| #27212348 | 2 |
| #27212346 | 2 |
| #27212345 | 2 |
| #27212342 | 2 |
| #27212324 | 2 |
| C22⋊Q8×C421 | 2 |
| #536 | 421 |