Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 80. C199 | #1467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263920 | 2 |
| #27164072 | 2 |
| #27163744 | 2 |
| #27163743 | 2 |
| #324×C199 | 2 |
| #1467 | 199 |