Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 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. #97×D197 | C2 | semidirect |
| 3. #27160819 | C2 | semidirect |
| 4. #27160818 | C2 | semidirect |
| 5. #329×C197 | C2 | semidirect |
| 15. #20263237 | C22 | semidirect |
| 18. #97×C197 | C22 | semidirect |
| 81. D197 | #329 | direct (N × H) |
| 82. C197 | C2×#329 | semidirect |
| 88. #329 | D197 | direct (N × H) |
| 101. #97 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×D197 | 2 |
| #97×D197 | 2 |
| #27160819 | 2 |
| #27160818 | 2 |
| #329×C197 | 2 |
| C2×#329 | 197 |