Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27164027 | C2 | semidirect |
| 5. #27163788 | C2 | semidirect |
| 6. #27163774 | C2 | semidirect |
| 7. #519×C199 | C2 | semidirect |
| 11. C2×#15691876 | C4 | semidirect |
| 12. C2×#15691873 | C4 | semidirect |
| 109. C199 | #1905 | semidirect |
| 112. #519 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263986 | 2 |
| #27164036 | 2 |
| #27164027 | 2 |
| #27163991 | 2 |
| #27163788 | 2 |
| #27163774 | 2 |
| #519×C199 | 2 |
| #1905 | 199 |