Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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. #27164058 | C2 | semidirect |
| 3. C2×#20263882 | C2 | semidirect |
| 4. C2×#20263871 | C2 | semidirect |
| 5. #27163919 | C2 | semidirect |
| 6. #27163779 | C2 | semidirect |
| 7. #417×C199 | C2 | semidirect |
| 38. #15691870 | D4 | semidirect |
| 130. C199 | #2037 | semidirect |
| 135. #417 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164582 | 2 |
| #27164058 | 2 |
| C2×#20263882 | 2 |
| C2×#20263871 | 2 |
| #27163919 | 2 |
| #27163779 | 2 |
| #417×C199 | 2 |
| #2037 | 199 |