Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. C2×#20263865 | C2 | semidirect |
| 5. #27163914 | C2 | semidirect |
| 6. #27163780 | C2 | semidirect |
| 7. #340×C199 | C2 | semidirect |
| 15. #20263877 | C4 | semidirect |
| 118. C199 | #1936 | semidirect |
| 126. #340 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263877 | 2 |
| C2×#20263875 | 2 |
| C2×#20263865 | 2 |
| #27163919 | 2 |
| #27163914 | 2 |
| #27163780 | 2 |
| #340×C199 | 2 |
| #1936 | 199 |