Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27164054 | C2 | semidirect |
| 3. #27164034 | C2 | semidirect |
| 4. #27163992 | C2 | semidirect |
| 5. #27163991 | C2 | semidirect |
| 6. #27163976 | C2 | semidirect |
| 7. #421×C199 | C2 | semidirect |
| 13. C2×#15691876 | C4 | semidirect |
| 14. C2×#15691874 | C4 | semidirect |
| 15. C2×#15691873 | C4 | semidirect |
| 16. C2×#15691871 | C4 | semidirect |
| 132. C199 | #1976 | semidirect |
| 137. #421 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263975 | 2 |
| #27164054 | 2 |
| #27164034 | 2 |
| #27163992 | 2 |
| #27163991 | 2 |
| #27163976 | 2 |
| #421×C199 | 2 |
| #1976 | 199 |