Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 15. #20263886 | C4 | semidirect |
| 59. C199⋊C8 | C4⋊C4 | semidirect |
| 98. C199 | #1944 | 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×#20263865 | 2 |
| #27163917 | 2 |
| #27163914 | 2 |
| #27163781 | 2 |
| #340×C199 | 2 |
| #1944 | 199 |