Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#15691358 | C2 | semidirect |
| 3. #27161097 | C2 | semidirect |
| 4. C2×#20263254 | C2 | semidirect |
| 5. #27161052 | C2 | semidirect |
| 6. #27160851 | C2 | semidirect |
| 7. #339×C197 | C2 | semidirect |
| 11. #20263359 | C4 | semidirect |
| 13. #20263354 | C4 | semidirect |
| 37. C2×Dic394 | C2×C4 | semidirect |
| 39. C2×D788 | C2×C4 | semidirect |
| 62. M16×C197 | C2×C4 | semidirect |
| 129. C197 | #1906 | semidirect |
| 137. #339 | D197 | semidirect |
| 185. M16 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161879 | 2 |
| C4×#15691358 | 2 |
| #27161097 | 2 |
| C2×#20263254 | 2 |
| #27161052 | 2 |
| #27160851 | 2 |
| #339×C197 | 2 |
| #1906 | 197 |