Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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. C22×#15691876 | C2 | semidirect |
| 3. C2×#20263874 | C2 | semidirect |
| 4. C2×#20263873 | C2 | semidirect |
| 6. #27163782 | C2 | semidirect |
| 122. C199 | #2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263985 | 2 |
| C22×#15691876 | 2 |
| C2×#20263874 | 2 |
| C2×#20263873 | 2 |
| #27163985 | 2 |
| #27163782 | 2 |
| C2×#137×C199 | 2 |
| #2020 | 199 |