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 |
|---|---|---|
| 2. #27164034 | C2 | semidirect |
| 3. #27164014 | C2 | semidirect |
| 4. #27163986 | C2 | semidirect |
| 5. #27163789 | C2 | semidirect |
| 6. #27163782 | C2 | semidirect |
| 7. #568×C199 | C2 | semidirect |
| 10. #20263985 | C4 | semidirect |
| 12. #20263980 | C4 | semidirect |
| 118. C199 | #1881 | semidirect |
| 121. #568 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164816 | 2 |
| #27164034 | 2 |
| #27164014 | 2 |
| #27163986 | 2 |
| #27163789 | 2 |
| #27163782 | 2 |
| #568×C199 | 2 |
| #1881 | 199 |