Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27164072 | C2 | semidirect |
| 3. #27163863 | C2 | semidirect |
| 4. #27163753 | C2 | semidirect |
| 5. #27163752 | C2 | semidirect |
| 6. #27163751 | C2 | semidirect |
| 7. #327×C199 | C2 | semidirect |
| 9. #20263954 | C4 | semidirect |
| 10. #20263951 | C4 | semidirect |
| 14. D4×Dic199 | C4 | semidirect |
| 15. #20263917 | C4 | semidirect |
| 119. C199 | #1505 | semidirect |
| 127. #327 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164563 | 2 |
| #27164072 | 2 |
| #27163863 | 2 |
| #27163753 | 2 |
| #27163752 | 2 |
| #27163751 | 2 |
| #327×C199 | 2 |
| #1505 | 199 |