Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#20263881 | C2 | semidirect |
| 3. #27164017 | C2 | semidirect |
| 4. C2×#20263871 | C2 | semidirect |
| 5. #27163919 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 7. #428×C199 | C2 | semidirect |
| 56. M16×C199 | D4 | semidirect |
| 130. C199 | #2037 | semidirect |
| 133. #428 | D199 | semidirect |
| 181. M16 | D796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164587 | 2 |
| C2×#20263881 | 2 |
| #27164017 | 2 |
| C2×#20263871 | 2 |
| #27163919 | 2 |
| #27163777 | 2 |
| #428×C199 | 2 |
| #2037 | 199 |