Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #27212360 | C2 | semidirect |
| 2. #27212358 | C2 | semidirect |
| 3. #27212354 | C2 | semidirect |
| 4. #27212349 | C2 | semidirect |
| 5. #27212345 | C2 | semidirect |
| 7. C4×Dic842 | C2 | semidirect |
| 8. C4×D1684 | C2 | semidirect |
| 9. C4×C22⋊D421 | C2 | semidirect |
| 10. #27212323 | C2 | semidirect |
| 11. C2×C42×C421 | C2 | semidirect |
| 74. C421 | #529 | semidirect |
| 86. C2×C42 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212360 | 2 |
| #27212358 | 2 |
| #27212354 | 2 |
| #27212349 | 2 |
| #27212345 | 2 |
| #27212340 | 2 |
| C4×Dic842 | 2 |
| C4×D1684 | 2 |
| C4×C22⋊D421 | 2 |
| #27212323 | 2 |
| C2×C42×C421 | 2 |
| #529 | 421 |