Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161807 | C2 | semidirect |
| 3. #27161429 | C2 | semidirect |
| 4. #27161386 | C2 | semidirect |
| 7. #27161286 | C2 | semidirect |
| 8. Q8×#13096802 | C2 | semidirect |
| 9. C4×#15691348 | C2 | semidirect |
| 115. C197 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161807 | 2 |
| #27161433 | 2 |
| #27161429 | 2 |
| #27161386 | 2 |
| #27161359 | 2 |
| #27161298 | 2 |
| #27161286 | 2 |
| Q8×#13096802 | 2 |
| C4×#15691348 | 2 |
| C4×#15691346 | 2 |
| #556×C197 | 2 |
| #3364 | 197 |