Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. #27163183 | C2 | direct (N × H) |
| 2. C2×#20263741 | C2 | semidirect |
| 3. C2×#20263740 | C2 | semidirect |
| 4. C2×D397⋊C8 | C2 | semidirect |
| 5. C22×#15691794 | C2 | semidirect |
| 7. #20263741 | C22 | semidirect |
| 8. #20263740 | C22 | semidirect |
| 9. D397⋊C8 | C22 | semidirect |
| 13. C2×#15691794 | C22 | semidirect |
| 46. C2×C397 | #131 | semidirect |
| 49. C397 | C2×#131 | semidirect |
| 97. C2 | #27163183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163183 | 2 |
| C2×#20263741 | 2 |
| C2×#20263740 | 2 |
| C2×D397⋊C8 | 2 |
| C22×#15691794 | 2 |
| C2×#20263730 | 2 |
| C2×#131 | 397 |