Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27164036 | C2 | semidirect |
| 3. #27164026 | C2 | semidirect |
| 4. #27164002 | C2 | semidirect |
| 5. #410×C199 | C2 | semidirect |
| 8. C2×#15691886 | C4 | semidirect |
| 12. C22×Dic398 | C4 | semidirect |
| 108. C199 | #1796 | semidirect |
| 114. #410 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264002 | 2 |
| #27164036 | 2 |
| #27164026 | 2 |
| #27164002 | 2 |
| #410×C199 | 2 |
| #1796 | 199 |