Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×C4×Dic398 | C2 | semidirect |
| 3. C2×#20263880 | C2 | semidirect |
| 6. #27163781 | C2 | semidirect |
| 7. #336×C199 | C2 | semidirect |
| 12. C2×#15691875 | C4 | semidirect |
| 72. Dic398 | C22⋊C4 | semidirect |
| 92. C2×C4×C199 | SD16 | semidirect |
| 132. C199 | #1880 | semidirect |
| 140. #336 | D199 | semidirect |
| 225. C2×C4 | #15691875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691875 | 2 |
| C2×C4×Dic398 | 2 |
| C2×#20263880 | 2 |
| C2×#20263877 | 2 |
| #27163920 | 2 |
| #27163781 | 2 |
| #336×C199 | 2 |
| #1880 | 199 |