Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27164035 | C2 | semidirect |
| 3. C2×#20263883 | C2 | semidirect |
| 4. #27163991 | C2 | semidirect |
| 5. #27163788 | C2 | semidirect |
| 6. #27163778 | C2 | semidirect |
| 7. C4×#41×C199 | C2 | semidirect |
| 10. #20263985 | C4 | semidirect |
| 12. #20263980 | C4 | semidirect |
| 33. C2×Dic398 | C2×C4 | semidirect |
| 34. C2×D796 | C2×C4 | semidirect |
| 44. #15691870 | C2×C4 | semidirect |
| 129. C199 | #1906 | semidirect |
| 132. C4×#41 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164816 | 2 |
| #27164035 | 2 |
| C2×#20263883 | 2 |
| #27163991 | 2 |
| #27163788 | 2 |
| #27163778 | 2 |
| C4×#41×C199 | 2 |
| #1906 | 199 |