Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27163992 | C2 | semidirect |
| 3. #27163812 | C2 | semidirect |
| 4. #27163810 | C2 | semidirect |
| 5. #410×C199 | C2 | semidirect |
| 6. C2×#15691886 | C4 | semidirect |
| 7. #20263953 | C4 | semidirect |
| 9. #20263944 | C4 | semidirect |
| 16. C2×C4×Dic199 | C4 | semidirect |
| 113. C199 | #2126 | semidirect |
| 117. #410 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164564 | 2 |
| #27163992 | 2 |
| #27163812 | 2 |
| #27163810 | 2 |
| #410×C199 | 2 |
| #2126 | 199 |