Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×#20263883 | C2 | semidirect |
| 3. C2×#20263882 | C2 | semidirect |
| 4. C2×#20263881 | C2 | semidirect |
| 5. M16×Dic199 | C2 | semidirect |
| 6. C4×Dic199⋊C4 | C2 | semidirect |
| 7. C2×#104×C199 | C2 | semidirect |
| 10. #20263953 | C4 | semidirect |
| 11. #20263951 | C4 | semidirect |
| 12. #20263944 | C4 | semidirect |
| 13. #20263942 | C4 | semidirect |
| 45. #15691870 | D4 | semidirect |
| 71. M16×C199 | D4 | semidirect |
| 140. Dic199 | #104 | semidirect |
| 148. C199 | #1980 | semidirect |
| 154. C2×#104 | D199 | semidirect |
| 206. M16 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164564 | 2 |
| C2×#20263883 | 2 |
| C2×#20263882 | 2 |
| C2×#20263881 | 2 |
| M16×Dic199 | 2 |
| C4×Dic199⋊C4 | 2 |
| C2×#104×C199 | 2 |
| #1980 | 199 |