Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161714 | C2 | semidirect |
| 2. #27161455 | C2 | semidirect |
| 3. #27161275 | C2 | semidirect |
| 4. #27160806 | C2 | semidirect |
| 5. #331×C197 | C2 | semidirect |
| 9. #20263323 | C22 | semidirect |
| 14. C4×#13096802 | C22 | semidirect |
| 16. C4⋊C8×C197 | C22 | semidirect |
| 43. D788 | D8 | semidirect |
| 74. C197 | #1619 | semidirect |
| 79. #331 | D197 | semidirect |
| 89. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161714 | 2 |
| #27161455 | 2 |
| #27161275 | 2 |
| #27160806 | 2 |
| #331×C197 | 2 |
| #1619 | 197 |