Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #27163973 | C2 | semidirect |
| 5. #27163790 | C2 | semidirect |
| 6. #27163788 | C2 | semidirect |
| 7. #405×C199 | C2 | semidirect |
| 15. C2×#15691869 | C4 | semidirect |
| 16. C2×C8×D199 | C4 | semidirect |
| 18. #20263873 | C4 | semidirect |
| 19. #20263871 | C4 | semidirect |
| 106. C199 | #1757 | semidirect |
| 112. #405 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263961 | 2 |
| #27164000 | 2 |
| #27163991 | 2 |
| #27163973 | 2 |
| #27163790 | 2 |
| #27163788 | 2 |
| #405×C199 | 2 |
| #1757 | 199 |