Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#20263877 | C2 | semidirect |
| 3. C2×#20263875 | C2 | semidirect |
| 4. C2×(C2×D199)⋊C8 | C2 | semidirect |
| 5. #27163875 | C2 | semidirect |
| 6. #27163780 | C2 | semidirect |
| 7. C2×#106×C199 | C2 | semidirect |
| 56. C2×C8×C199 | D4 | semidirect |
| 143. C199 | #2034 | semidirect |
| 146. C2×#106 | D199 | semidirect |
| 196. C2×C8 | D796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263930 | 2 |
| C2×#20263877 | 2 |
| C2×#20263875 | 2 |
| C2×(C2×D199)⋊C8 | 2 |
| #27163875 | 2 |
| #27163780 | 2 |
| C2×#106×C199 | 2 |
| #2034 | 199 |