Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27161043 | C2 | semidirect |
| 2. #27160805 | C2 | semidirect |
| 3. #27160803 | C2 | semidirect |
| 50. C23×C197 | M16 | semidirect |
| 67. C2×C4×C197 | M16 | semidirect |
| 97. C197 | #1465 | semidirect |
| 147. C23 | #15691342 | semidirect |
| 164. C2×C4 | #15691342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161043 | 2 |
| #27160805 | 2 |
| #27160803 | 2 |
| C2×C4×D4×C197 | 2 |
| #1465 | 197 |