Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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×#20263869 | C2 | semidirect |
| 3. #27163898 | C2 | semidirect |
| 4. #27163895 | C2 | semidirect |
| 5. C2×#99×C199 | C2 | semidirect |
| 8. #20264000 | C4 | semidirect |
| 14. C23×Dic199 | C22 | semidirect |
| 16. C2×C22⋊Dic199 | C22 | semidirect |
| 22. C2×C22⋊C4×C199 | C22 | semidirect |
| 70. C22×D199 | C22⋊C4 | semidirect |
| 89. C2×Dic199 | C22⋊C4 | semidirect |
| 97. C23×C199 | C22⋊C4 | semidirect |
| 110. C2×C4×C199 | C22⋊C4 | semidirect |
| 148. C199 | #1790 | semidirect |
| 152. C2×#99 | D199 | semidirect |
| 168. C2×C22⋊C4 | C2×D199 | semidirect |
| 226. C23 | (C2×D199)⋊C4 | semidirect |
| 259. C2×C4 | (C2×D199)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264000 | 2 |
| C2×#20263869 | 2 |
| #27163898 | 2 |
| #27163895 | 2 |
| C2×#99×C199 | 2 |
| #1790 | 199 |