Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 59. C2×C4×C197 | Q16 | semidirect |
| 78. C197 | #1605 | semidirect |
| 137. C2×C4 | #15691348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161710 | 2 |
| #27161235 | 2 |
| #27160815 | 2 |
| #27160805 | 2 |
| #395×C197 | 2 |
| #1605 | 197 |