Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 52. Dic398 | Q16 | semidirect |
| 59. Q8×C199 | Q16 | semidirect |
| 82. C199 | #1633 | semidirect |
| 137. Q8 | Dic796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic398 | 2 |
| #27164398 | 2 |
| #27164314 | 2 |
| #27164313 | 2 |
| #27163766 | 2 |
| #27163750 | 2 |
| Q8⋊C8×C199 | 2 |
| #1633 | 199 |