Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #27163184 | C2 | semidirect |
| 2. #27163183 | C2 | semidirect |
| 3. #27163167 | C2 | semidirect |
| 4. #27163161 | C2 | semidirect |
| 5. #27163160 | C2 | semidirect |
| 6. #27163150 | C2 | semidirect |
| 18. #20263721 | C4 | semidirect |
| 19. #20263720 | C4 | semidirect |
| 20. #20263716 | C4 | semidirect |
| 22. SD16×C397 | C4 | semidirect |
| 51. C397 | #444 | semidirect |
| 64. SD16 | #13097544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163184 | 2 |
| #27163183 | 2 |
| #27163167 | 2 |
| #27163161 | 2 |
| #27163160 | 2 |
| #27163150 | 2 |
| #27163117 | 2 |
| #444 | 397 |