Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20263326 | C2 | semidirect |
| 3. #27161289 | C2 | semidirect |
| 4. #27161284 | C2 | semidirect |
| 5. #27161103 | C2 | semidirect |
| 6. #27161087 | C2 | semidirect |
| 89. C4×C197 | #137 | semidirect |
| 97. C197 | #3039 | semidirect |
| 188. C4 | #20263356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C2×#20263326 | 2 |
| #27161289 | 2 |
| #27161284 | 2 |
| #27161103 | 2 |
| #27161087 | 2 |
| C4×#41×C197 | 2 |
| #3039 | 197 |