Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161445 | C2 | semidirect |
| 3. #27161427 | C2 | semidirect |
| 4. #27161083 | C2 | semidirect |
| 5. C4×#15691342 | C2 | semidirect |
| 6. #533×C197 | C2 | semidirect |
| 13. #20263246 | C22 | semidirect |
| 14. #20263237 | C22 | semidirect |
| 15. C4×#13096802 | C22 | semidirect |
| 16. C4⋊Q8×C197 | C22 | semidirect |
| 17. #125×C197 | C22 | semidirect |
| 74. C197 | #3138 | semidirect |
| 76. #533 | D197 | semidirect |
| 85. C4⋊Q8 | C2×D197 | semidirect |
| 89. #125 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263323 | 2 |
| #27161445 | 2 |
| #27161427 | 2 |
| #27161083 | 2 |
| C4×#15691342 | 2 |
| #533×C197 | 2 |
| #3138 | 197 |