Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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. #27163845 | C2 | semidirect |
| 4. #27163843 | C2 | semidirect |
| 7. #20263895 | C4 | semidirect |
| 20. C199⋊C16 | C2×C4 | semidirect |
| 55. C199 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263895 | 2 |
| #27164056 | 2 |
| #27163845 | 2 |
| #27163843 | 2 |
| C2×#107×C199 | 2 |
| #2159 | 199 |