Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 1. #27164066 | C2 | semidirect |
| 2. #27164041 | C2 | semidirect |
| 5. #27163789 | C2 | semidirect |
| 6. #27163779 | C2 | semidirect |
| 15. #20263882 | C4 | semidirect |
| 16. #20263882 | C4 | semidirect |
| 97. C199 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164066 | 2 |
| #27164041 | 2 |
| #27164035 | 2 |
| C2×#20263882 | 2 |
| #27163789 | 2 |
| #27163779 | 2 |
| #568×C199 | 2 |
| #1861 | 199 |