Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
264 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 81 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. #27164075 | C2 | semidirect |
| 2. C4×#15691870 | C2 | semidirect |
| 3. #27163758 | C2 | semidirect |
| 8. #20263866 | C22 | semidirect |
| 9. #20263866 | C22 | semidirect |
| 84. C199 | #1527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164075 | 2 |
| C4×#15691870 | 2 |
| #27163758 | 2 |
| C2×#124×C199 | 2 |
| #1527 | 199 |