Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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. #27161554 | C2 | semidirect |
| 3. #27161095 | C2 | semidirect |
| 4. #27161052 | C2 | semidirect |
| 5. #27160851 | C2 | semidirect |
| 6. #27160835 | C2 | semidirect |
| 7. #418×C197 | C2 | semidirect |
| 11. C2×#15691346 | C4 | semidirect |
| 12. C2×#15691343 | C4 | semidirect |
| 29. C2×Dic394 | C2×C4 | semidirect |
| 30. C2×D788 | C2×C4 | semidirect |
| 38. C2×#13096802 | C2×C4 | semidirect |
| 115. C197 | #1904 | semidirect |
| 120. #418 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| #27161554 | 2 |
| #27161095 | 2 |
| #27161052 | 2 |
| #27160851 | 2 |
| #27160835 | 2 |
| #418×C197 | 2 |
| #1904 | 197 |