Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#20269760 | C2 | semidirect |
| 2. C2×#20269754 | C2 | semidirect |
| 3. #27212346 | C2 | semidirect |
| 5. #27212289 | C2 | semidirect |
| 6. #27212286 | C2 | semidirect |
| 7. #107×C421 | C2 | semidirect |
| 36. C8×C421 | D4 | semidirect |
| 55. C421 | #468 | semidirect |
| 61. #107 | D421 | semidirect |
| 92. C8 | D1684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269760 | 2 |
| C2×#20269754 | 2 |
| #27212346 | 2 |
| #27212341 | 2 |
| #27212289 | 2 |
| #27212286 | 2 |
| #107×C421 | 2 |
| #468 | 421 |