Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 46. C199⋊C8 | Q16 | semidirect |
| 70. C199 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164414 | 2 |
| #27164228 | 2 |
| #27164149 | 2 |
| #27163770 | 2 |
| #27163767 | 2 |
| #27163765 | 2 |
| #477×C199 | 2 |
| #1692 | 199 |