Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 3. C2×#20263879 | C2 | semidirect |
| 5. #27163781 | C2 | semidirect |
| 6. #27163780 | C2 | semidirect |
| 7. C2×#103×C199 | C2 | semidirect |
| 11. #20263931 | C4 | semidirect |
| 131. C199 | #1873 | semidirect |
| 136. C2×#103 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263931 | 2 |
| C2×#20263913 | 2 |
| C2×#20263879 | 2 |
| C2×(C2×D199)⋊C8 | 2 |
| #27163781 | 2 |
| #27163780 | 2 |
| C2×#103×C199 | 2 |
| #1873 | 199 |