Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27163144 | C2 | semidirect |
| 2. #27163143 | C2 | semidirect |
| 3. #27163129 | C2 | semidirect |
| 4. #27163128 | C2 | semidirect |
| 5. #27163125 | C2 | semidirect |
| 6. #27163117 | C2 | semidirect |
| 7. #27163116 | C2 | semidirect |
| 8. C2×#20263721 | C2 | semidirect |
| 9. Q16×D397 | C2 | semidirect |
| 10. #27163104 | C2 | semidirect |
| 11. #137×C397 | C2 | semidirect |
| 87. C397 | #578 | semidirect |
| 94. #137 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163144 | 2 |
| #27163143 | 2 |
| #27163129 | 2 |
| #27163128 | 2 |
| #27163125 | 2 |
| #27163117 | 2 |
| #27163116 | 2 |
| C2×#20263721 | 2 |
| Q16×D397 | 2 |
| #27163104 | 2 |
| #137×C397 | 2 |
| #578 | 397 |