Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#20263888 | C2 | semidirect |
| 3. C2×#20263878 | C2 | semidirect |
| 5. C2×#20263866 | C2 | semidirect |
| 6. #27163924 | C2 | semidirect |
| 11. C2×#15691874 | C4 | semidirect |
| 66. C199⋊C8 | C22⋊C4 | semidirect |
| 112. C199 | #1973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691874 | 2 |
| C2×#20263888 | 2 |
| C2×#20263878 | 2 |
| C2×#20263876 | 2 |
| C2×#20263866 | 2 |
| #27163924 | 2 |
| #390×C199 | 2 |
| #1973 | 199 |