Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
278 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 278 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 |
|---|---|---|
| 1. C2×#20263890 | C2 | semidirect |
| 4. #27163782 | C2 | semidirect |
| 71. C22×C199 | #108 | semidirect |
| 85. C199 | #1855 | semidirect |
| 157. C22 | #20263890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263890 | 2 |
| #27163982 | 2 |
| C2×C22⋊(C199⋊C8) | 2 |
| #27163782 | 2 |
| C22×M16×C199 | 2 |
| #1855 | 199 |