Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
194 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 59. Q8×C199 | Q16 | semidirect |
| 83. C199 | #1648 | semidirect |
| 139. Q8 | #15691876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164421 | 2 |
| #27164303 | 2 |
| #27164228 | 2 |
| #27163764 | 2 |
| Q8⋊(C199⋊C8) | 2 |
| #557×C199 | 2 |
| #1648 | 199 |