Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27161484 | C2 | semidirect |
| 2. #27161482 | C2 | semidirect |
| 3. #27161458 | C2 | semidirect |
| 6. #27160801 | C2 | semidirect |
| 69. C197 | #1722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161484 | 2 |
| #27161482 | 2 |
| #27161458 | 2 |
| #27161451 | 2 |
| #27161425 | 2 |
| #27160801 | 2 |
| #486×C197 | 2 |
| #1722 | 197 |