Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #27160830 | C2 | semidirect |
| 4. #27160829 | C2 | semidirect |
| 5. #334×C197 | C2 | semidirect |
| 43. #13096802 | M16 | semidirect |
| 49. C8×C197 | M16 | semidirect |
| 65. C197 | #1566 | semidirect |
| 71. #334 | D197 | semidirect |
| 115. C8 | #15691341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161101 | 2 |
| C4×C8×D197 | 2 |
| #27160830 | 2 |
| #27160829 | 2 |
| #334×C197 | 2 |
| #1566 | 197 |