Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
234 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 83 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×#20269750 | C2 | semidirect |
| 4. #27212273 | C2 | semidirect |
| 11. C22⋊Dic421 | C4 | semidirect |
| 21. C2×Dic421 | C2×C4 | semidirect |
| 37. C22×C421 | C4⋊C4 | semidirect |
| 53. C421 | #385 | semidirect |
| 91. C22 | #20269750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic421 | 2 |
| C2×#20269750 | 2 |
| C2×C22⋊Dic421 | 2 |
| #27212273 | 2 |
| C2×C22⋊C4×C421 | 2 |
| #385 | 421 |