Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 1. C2×#20263334 | C2 | semidirect |
| 3. #27161156 | C2 | semidirect |
| 4. #27161144 | C2 | semidirect |
| 5. #27161047 | C2 | semidirect |
| 6. C2×C4×#13096802 | C2 | semidirect |
| 7. #423×C197 | C2 | semidirect |
| 34. C2×#13096802 | D4 | semidirect |
| 75. C4×C197 | #131 | semidirect |
| 83. C197 | #2931 | semidirect |
| 89. #423 | D197 | semidirect |
| 160. C4 | #20263334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263334 | 2 |
| #27161629 | 2 |
| #27161156 | 2 |
| #27161144 | 2 |
| #27161047 | 2 |
| C2×C4×#13096802 | 2 |
| #423×C197 | 2 |
| #2931 | 197 |