Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 1. C2×#20269758 | C2 | semidirect |
| 2. C2×#20269754 | C2 | semidirect |
| 3. #27212342 | C2 | semidirect |
| 5. #27212299 | C2 | semidirect |
| 6. #27212288 | C2 | semidirect |
| 7. #103×C421 | C2 | semidirect |
| 30. #16809890 | D4 | semidirect |
| 55. C421 | #468 | semidirect |
| 62. #103 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269758 | 2 |
| C2×#20269754 | 2 |
| #27212342 | 2 |
| #27212341 | 2 |
| #27212299 | 2 |
| #27212288 | 2 |
| #103×C421 | 2 |
| #468 | 421 |