Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
752 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #27161086 | C2 | direct (N × H) |
| 5. C2×#20263251 | C2 | semidirect |
| 6. C2×#20263250 | C2 | semidirect |
| 7. C2×#20263249 | C2 | semidirect |
| 8. C2×#103×C197 | C2 | semidirect |
| 13. C2×Q8×D197 | C4 | semidirect |
| 25. #20263251 | C22 | semidirect |
| 26. #20263250 | C22 | semidirect |
| 27. #20263249 | C22 | semidirect |
| 31. #103×C197 | C22 | semidirect |
| 41. Q8×D197 | C2×C4 | semidirect |
| 117. C2×C197 | #419 | semidirect |
| 122. C197 | C2×#419 | semidirect |
| 131. C2×#103 | D197 | semidirect |
| 154. #103 | C2×D197 | semidirect |
| 241. C2 | #27161086 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D197 | 2 |
| C22×#15691341 | 2 |
| C2×#20263284 | 2 |
| #27161086 | 2 |
| C2×#20263251 | 2 |
| C2×#20263250 | 2 |
| C2×#20263249 | 2 |
| C2×#103×C197 | 2 |
| C2×#419 | 197 |