Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 13. #20263866 | C4 | semidirect |
| 20. C4⋊C8×C199 | C4 | semidirect |
| 52. C199⋊C8 | C4⋊C4 | semidirect |
| 84. C199 | #1771 | semidirect |
| 101. C4⋊C8 | Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263866 | 2 |
| C2×#20263865 | 2 |
| C2×C8×Dic199 | 2 |
| C4×C4⋊Dic199 | 2 |
| #27163772 | 2 |
| C2×C4⋊C8×C199 | 2 |
| #1771 | 199 |