Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27164026 | C2 | semidirect |
| 4. C2×#20263873 | C2 | semidirect |
| 6. #27163783 | C2 | semidirect |
| 7. #424×C199 | C2 | semidirect |
| 100. C199 | #2046 | semidirect |
| 103. #424 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691875 | 2 |
| #27164026 | 2 |
| #27164022 | 2 |
| C2×#20263873 | 2 |
| C2×#20263871 | 2 |
| #27163783 | 2 |
| #424×C199 | 2 |
| #2046 | 199 |