Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #41×Dic197 | C2 | semidirect |
| 3. C2×#20263252 | C2 | semidirect |
| 4. #27161052 | C2 | semidirect |
| 5. #27160850 | C2 | semidirect |
| 6. #27160838 | C2 | semidirect |
| 7. #421×C197 | C2 | semidirect |
| 10. #20263356 | C4 | semidirect |
| 12. #20263351 | C4 | semidirect |
| 33. C2×Dic394 | C2×C4 | semidirect |
| 34. C2×D788 | C2×C4 | semidirect |
| 44. #15691342 | C2×C4 | semidirect |
| 129. C197 | #1906 | semidirect |
| 133. #421 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| #41×Dic197 | 2 |
| C2×#20263252 | 2 |
| #27161052 | 2 |
| #27160850 | 2 |
| #27160838 | 2 |
| #421×C197 | 2 |
| #1906 | 197 |