Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
274 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. C2×#20263888 | C2 | semidirect |
| 2. C2×#20263886 | C2 | semidirect |
| 5. #27163884 | C2 | semidirect |
| 6. #27163773 | C2 | semidirect |
| 99. C199 | #2092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263888 | 2 |
| C2×#20263886 | 2 |
| C2×#20263876 | 2 |
| #27163884 | 2 |
| #27163773 | 2 |
| #390×C199 | 2 |
| #2092 | 199 |