Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 346 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. #27161554 | C2 | semidirect |
| 2. #27161096 | C2 | semidirect |
| 3. #27161084 | C2 | semidirect |
| 4. #27161053 | C2 | semidirect |
| 5. #27160850 | C2 | semidirect |
| 6. #27160836 | C2 | semidirect |
| 22. C2×SD16×C197 | C4 | semidirect |
| 23. C2×D8×C197 | C4 | semidirect |
| 44. C2×Q8×C197 | C2×C4 | semidirect |
| 50. C2×D4×C197 | C2×C4 | semidirect |
| 59. C2×C8×C197 | C2×C4 | semidirect |
| 115. C197 | #1904 | semidirect |
| 128. C2×SD16 | Dic197 | semidirect |
| 129. C2×D8 | Dic197 | semidirect |
| 146. C2×Q8 | C2×Dic197 | semidirect |
| 152. C2×D4 | C2×Dic197 | semidirect |
| 165. C2×C8 | C2×Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161554 | 2 |
| #27161096 | 2 |
| #27161084 | 2 |
| #27161053 | 2 |
| #27160850 | 2 |
| #27160836 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #1904 | 197 |