Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #27161514 | C2 | semidirect |
| 2. #27161332 | C2 | semidirect |
| 3. #27160889 | C2 | semidirect |
| 4. #27160861 | C2 | semidirect |
| 5. #575×C197 | C2 | semidirect |
| 6. C2×D1576 | C22 | semidirect |
| 10. #20263266 | C22 | semidirect |
| 11. #20263258 | C22 | semidirect |
| 35. Q16×C197 | D4 | semidirect |
| 39. D8×C197 | D4 | semidirect |
| 83. C197 | #2190 | semidirect |
| 85. #575 | D197 | semidirect |
| 115. Q16 | C22⋊D197 | semidirect |
| 120. D8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161514 | 2 |
| #27161332 | 2 |
| #27160889 | 2 |
| #27160861 | 2 |
| #575×C197 | 2 |
| #2190 | 197 |