Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D397 | C2 | semidirect |
| 3. #27163095 | C2 | semidirect |
| 4. #27163082 | C2 | semidirect |
| 5. #27163081 | C2 | semidirect |
| 6. #27163078 | C2 | semidirect |
| 7. #27163076 | C2 | semidirect |
| 8. #27163075 | C2 | semidirect |
| 9. #27163072 | C2 | semidirect |
| 10. #27163054 | C2 | semidirect |
| 11. C22⋊Q8×C397 | C2 | semidirect |
| 83. C397 | #536 | semidirect |
| 94. C22⋊Q8 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263731 | 2 |
| C2×Q8×D397 | 2 |
| #27163095 | 2 |
| #27163082 | 2 |
| #27163081 | 2 |
| #27163078 | 2 |
| #27163076 | 2 |
| #27163075 | 2 |
| #27163072 | 2 |
| #27163054 | 2 |
| C22⋊Q8×C397 | 2 |
| #536 | 397 |