Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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. #27164041 | C2 | semidirect |
| 4. C4×Dic199⋊C4 | C2 | semidirect |
| 5. #27163779 | C2 | semidirect |
| 6. #27163778 | C2 | semidirect |
| 9. Q8×Dic199 | C4 | semidirect |
| 10. Q8×Dic199 | C4 | semidirect |
| 13. D4×Dic199 | C4 | semidirect |
| 14. D4×Dic199 | C4 | semidirect |
| 86. Q8×C199 | C4⋊C4 | semidirect |
| 90. D4×C199 | C4⋊C4 | semidirect |
| 124. Dic199 | #104 | semidirect |
| 131. C199 | #1806 | semidirect |
| 204. Q8 | Dic199⋊C4 | semidirect |
| 208. D4 | Dic199⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic199 | 2 |
| #27164041 | 2 |
| C2×#20263882 | 2 |
| C4×Dic199⋊C4 | 2 |
| #27163779 | 2 |
| #27163778 | 2 |
| C2×#104×C199 | 2 |
| #1806 | 199 |