Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#20263880 | C2 | semidirect |
| 3. C2×#20263877 | C2 | semidirect |
| 4. #27163878 | C2 | semidirect |
| 5. C2×C22⋊C8×C199 | C2 | semidirect |
| 9. C2×#15691886 | C4 | semidirect |
| 60. Dic398 | C22⋊C4 | semidirect |
| 63. D796 | C22⋊C4 | semidirect |
| 115. C199 | #1788 | semidirect |
| 120. C2×C22⋊C8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691886 | 2 |
| C2×#20263880 | 2 |
| C2×#20263877 | 2 |
| #27163878 | 2 |
| C2×C22⋊C8×C199 | 2 |
| #1788 | 199 |