Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. #27161083 | C2 | semidirect |
| 3. C2×#20263243 | C2 | semidirect |
| 4. #27160838 | C2 | semidirect |
| 5. #518×C197 | C2 | semidirect |
| 10. #20263322 | C4 | semidirect |
| 22. C2×D788 | C2×C4 | semidirect |
| 30. C4×Dic197 | C2×C4 | semidirect |
| 38. C4⋊C4×C197 | D4 | semidirect |
| 87. C197 | #1887 | semidirect |
| 90. #518 | D197 | semidirect |
| 124. C4⋊C4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263322 | 2 |
| #27161083 | 2 |
| C2×#20263243 | 2 |
| #27160838 | 2 |
| #518×C197 | 2 |
| #1887 | 197 |