Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20263326 | C2 | semidirect |
| 3. #27161375 | C2 | semidirect |
| 4. #27161370 | C2 | semidirect |
| 5. #27161365 | C2 | semidirect |
| 6. #27161360 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 9. #423×C197 | C2 | semidirect |
| 36. #15691358 | Q8 | semidirect |
| 74. Dic394 | C2×Q8 | semidirect |
| 76. D788 | C2×Q8 | semidirect |
| 121. C197 | #3079 | semidirect |
| 130. #423 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263326 | 2 |
| C4×#15691358 | 2 |
| #27161375 | 2 |
| #27161370 | 2 |
| #27161365 | 2 |
| #27161360 | 2 |
| #27161121 | 2 |
| #27161081 | 2 |
| #423×C197 | 2 |
| #3079 | 197 |