Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 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. #27164493 | C2 | semidirect |
| 3. #27164034 | C2 | semidirect |
| 4. #27163991 | C2 | semidirect |
| 5. #27163790 | C2 | semidirect |
| 6. #27163774 | C2 | semidirect |
| 7. #418×C199 | C2 | semidirect |
| 11. C2×#15691874 | C4 | semidirect |
| 12. C2×#15691871 | C4 | semidirect |
| 29. C2×Dic398 | C2×C4 | semidirect |
| 30. C2×D796 | C2×C4 | semidirect |
| 38. C2×C199⋊C8 | C2×C4 | semidirect |
| 115. C199 | #1904 | semidirect |
| 120. #418 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263981 | 2 |
| #27164493 | 2 |
| #27164034 | 2 |
| #27163991 | 2 |
| #27163790 | 2 |
| #27163774 | 2 |
| #418×C199 | 2 |
| #1904 | 199 |