Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D421 | C2 | semidirect |
| 3. #27212297 | C2 | semidirect |
| 4. #27212288 | C2 | semidirect |
| 5. #27212286 | C2 | semidirect |
| 6. #27212278 | C2 | semidirect |
| 7. #106×C421 | C2 | semidirect |
| 52. C421 | #481 | semidirect |
| 57. #106 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212341 | 2 |
| C4⋊C4×D421 | 2 |
| #27212297 | 2 |
| #27212288 | 2 |
| #27212286 | 2 |
| #27212278 | 2 |
| #106×C421 | 2 |
| #481 | 421 |