Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#20263334 | C2 | semidirect |
| 3. #27161149 | C2 | semidirect |
| 4. #27161047 | C2 | semidirect |
| 5. C2×#20263237 | C2 | semidirect |
| 6. #423×C197 | C2 | semidirect |
| 32. C2×#13096802 | D4 | semidirect |
| 79. C197 | #2932 | semidirect |
| 84. #423 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263334 | 2 |
| #27161629 | 2 |
| #27161149 | 2 |
| #27161047 | 2 |
| C2×#20263237 | 2 |
| #423×C197 | 2 |
| #2932 | 197 |