Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
308 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 308 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×#20263873 | C2 | semidirect |
| 4. #27163790 | C2 | semidirect |
| 80. C199 | #1915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164589 | 2 |
| #27164002 | 2 |
| C2×#20263873 | 2 |
| #27163790 | 2 |
| #568×C199 | 2 |
| #1915 | 199 |