Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27212414 | C2 | semidirect |
| 2. #27212413 | C2 | semidirect |
| 3. #27212399 | C2 | semidirect |
| 4. #27212398 | C2 | semidirect |
| 5. #27212395 | C2 | semidirect |
| 6. #27212387 | C2 | semidirect |
| 7. #27212386 | C2 | semidirect |
| 8. C2×#20269761 | C2 | semidirect |
| 9. Q16×D421 | C2 | semidirect |
| 10. #27212374 | C2 | semidirect |
| 11. #137×C421 | C2 | semidirect |
| 87. C421 | #578 | semidirect |
| 94. #137 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212414 | 2 |
| #27212413 | 2 |
| #27212399 | 2 |
| #27212398 | 2 |
| #27212395 | 2 |
| #27212387 | 2 |
| #27212386 | 2 |
| C2×#20269761 | 2 |
| Q16×D421 | 2 |
| #27212374 | 2 |
| #137×C421 | 2 |
| #578 | 421 |