Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27161846 | C2 | semidirect |
| 2. #27161096 | C2 | semidirect |
| 3. #27161084 | C2 | semidirect |
| 4. C2×#20263243 | C2 | semidirect |
| 5. #27160850 | C2 | semidirect |
| 6. #27160837 | C2 | semidirect |
| 22. C2×SD16×C197 | C4 | semidirect |
| 23. C2×D8×C197 | C4 | semidirect |
| 112. C197 | #1903 | semidirect |
| 125. C2×SD16 | Dic197 | semidirect |
| 126. C2×D8 | Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161846 | 2 |
| #27161096 | 2 |
| #27161084 | 2 |
| C2×#20263243 | 2 |
| #27160850 | 2 |
| #27160837 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #1903 | 197 |