Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
168 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 62. C199 | #1710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164421 | 2 |
| #27164370 | 2 |
| #27164369 | 2 |
| #27164368 | 2 |
| C8×C199⋊C8 | 2 |
| #487×C199 | 2 |
| #1710 | 199 |