Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27164370 | C2 | semidirect |
| 3. #27164368 | C2 | semidirect |
| 6. #27163740 | C2 | semidirect |
| 7. #500×C199 | C2 | semidirect |
| 68. C199 | #1719 | semidirect |
| 70. #500 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164392 | 2 |
| #27164370 | 2 |
| #27164368 | 2 |
| #27164366 | 2 |
| #27164365 | 2 |
| #27163740 | 2 |
| #500×C199 | 2 |
| #1719 | 199 |