Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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×C4⋊(C199⋊C8) | C2 | semidirect |
| 3. C2×#20263876 | C2 | semidirect |
| 4. C2×#20263875 | C2 | semidirect |
| 5. #27163920 | C2 | semidirect |
| 6. #27163780 | C2 | semidirect |
| 7. #390×C199 | C2 | semidirect |
| 97. C2×C4×C199 | D8 | semidirect |
| 142. C199 | #2054 | semidirect |
| 149. #390 | D199 | semidirect |
| 238. C2×C4 | #15691871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691871 | 2 |
| C2×C4⋊(C199⋊C8) | 2 |
| C2×#20263876 | 2 |
| C2×#20263875 | 2 |
| #27163920 | 2 |
| #27163780 | 2 |
| #390×C199 | 2 |
| #2054 | 199 |