Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
184 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 184 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 |
|---|---|---|
| 9. #20263891 | C4 | semidirect |
| 60. C199 | #1953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164066 | 2 |
| C2×#20263891 | 2 |
| #27163973 | 2 |
| #27163789 | 2 |
| C2×#108×C199 | 2 |
| #1953 | 199 |