Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×C22⋊Dic199 | C2 | semidirect |
| 4. #27163784 | C2 | semidirect |
| 5. C4×C22⋊C4×C199 | C2 | semidirect |
| 7. C22×C4×D199 | C4 | semidirect |
| 12. C2×Dic199⋊C4 | C4 | semidirect |
| 15. C2×(C2×D199)⋊C4 | C4 | semidirect |
| 17. C2×C4×Dic199 | C4 | semidirect |
| 18. #20263869 | C4 | direct (N × H) |
| 41. C22⋊Dic199 | C2×C4 | semidirect |
| 57. C22⋊C4×C199 | C2×C4 | semidirect |
| 63. C22×D199 | C42 | semidirect |
| 75. C2×Dic199 | C42 | semidirect |
| 120. C4×C199 | #99 | semidirect |
| 133. C199 | C4×#99 | semidirect |
| 138. C4×C22⋊C4 | D199 | semidirect |
| 188. C22⋊C4 | C4×D199 | semidirect |
| 258. C4 | #20263869 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D199 | 2 |
| C2×#20263869 | 2 |
| C4×C22⋊Dic199 | 2 |
| #27163784 | 2 |
| C4×C22⋊C4×C199 | 2 |
| C4×#99 | 199 |