Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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×#20263891 | C2 | semidirect |
| 3. C2×#20263883 | C2 | semidirect |
| 4. #27163984 | C2 | semidirect |
| 5. C2×C4×C8×C199 | C2 | semidirect |
| 9. C2×Dic796 | C4 | semidirect |
| 10. C2×#15691875 | C4 | semidirect |
| 11. C2×D1592 | C4 | semidirect |
| 85. C199 | #1974 | semidirect |
| 91. C2×C4×C8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263977 | 2 |
| C2×#20263891 | 2 |
| C2×#20263883 | 2 |
| #27163984 | 2 |
| C2×C4×C8×C199 | 2 |
| #1974 | 199 |