Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 62. C4×C199 | #108 | semidirect |
| 72. C199 | #1950 | semidirect |
| 135. C4 | #20263890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263890 | 2 |
| #27164042 | 2 |
| C2×C4⋊(C199⋊C8) | 2 |
| #27163782 | 2 |
| C4×M16×C199 | 2 |
| #1950 | 199 |