Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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. #27161667 | C2 | semidirect |
| 2. #27161230 | C2 | semidirect |
| 3. #27161213 | C2 | semidirect |
| 4. #27160815 | C2 | semidirect |
| 5. #27160812 | C2 | semidirect |
| 6. #27160803 | C2 | semidirect |
| 7. #392×C197 | C2 | semidirect |
| 27. C2×Dic394 | D4 | semidirect |
| 28. C2×D788 | D4 | semidirect |
| 37. C4⋊Dic197 | D4 | semidirect |
| 38. C4⋊Dic197 | D4 | semidirect |
| 135. C197 | #1600 | semidirect |
| 140. #392 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161667 | 2 |
| #27161230 | 2 |
| #27161213 | 2 |
| #27160815 | 2 |
| #27160812 | 2 |
| #27160803 | 2 |
| #392×C197 | 2 |
| #1600 | 197 |