Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 3. #27160816 | C2 | semidirect |
| 4. #27160805 | C2 | semidirect |
| 5. #544×C197 | C2 | semidirect |
| 64. C2×C4×C197 | SD16 | semidirect |
| 90. C197 | #1599 | semidirect |
| 92. #544 | D197 | semidirect |
| 154. C2×C4 | #15691345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161229 | 2 |
| #27160996 | 2 |
| #27160816 | 2 |
| #27160805 | 2 |
| #544×C197 | 2 |
| #1599 | 197 |