Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
316 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 113 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×#20263889 | C2 | semidirect |
| 3. C2×#20263887 | C2 | semidirect |
| 5. #27163781 | C2 | semidirect |
| 6. #27163781 | C2 | semidirect |
| 23. C22⋊C8×C199 | C4 | semidirect |
| 120. C199 | #1854 | semidirect |
| 143. C22⋊C8 | Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263914 | 2 |
| C2×#20263889 | 2 |
| C2×#20263887 | 2 |
| #27163878 | 2 |
| #27163781 | 2 |
| C2×C22⋊C8×C199 | 2 |
| #1854 | 199 |