Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27163091 | C2 | semidirect |
| 2. #27163087 | C2 | semidirect |
| 3. #27163085 | C2 | semidirect |
| 4. #27163081 | C2 | semidirect |
| 5. #27163072 | C2 | semidirect |
| 7. C4×D1588 | C2 | semidirect |
| 8. C4×D1588 | C2 | semidirect |
| 9. #27163053 | C2 | semidirect |
| 10. C42×D397 | C2 | semidirect |
| 11. C4×Q8×C397 | C2 | semidirect |
| 74. C397 | #529 | semidirect |
| 82. C4×Q8 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163091 | 2 |
| #27163087 | 2 |
| #27163085 | 2 |
| #27163081 | 2 |
| #27163072 | 2 |
| #27163071 | 2 |
| C4×D1588 | 2 |
| #27163053 | 2 |
| C42×D397 | 2 |
| C4×Q8×C397 | 2 |
| #529 | 397 |