Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #27161560 | C2 | semidirect |
| 3. C2×#20263254 | C2 | semidirect |
| 4. #27161084 | C2 | semidirect |
| 5. #27160848 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 7. #390×C197 | C2 | semidirect |
| 10. #20263352 | C4 | semidirect |
| 42. #15691342 | C2×C4 | semidirect |
| 58. C2×D4×C197 | C2×C4 | semidirect |
| 69. Dic394 | C22⋊C4 | semidirect |
| 71. D788 | C22⋊C4 | semidirect |
| 132. C197 | #1883 | semidirect |
| 138. #390 | D197 | semidirect |
| 174. C2×D4 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263352 | 2 |
| #27161560 | 2 |
| C2×#20263254 | 2 |
| #27161084 | 2 |
| #27160848 | 2 |
| #27160839 | 2 |
| #390×C197 | 2 |
| #1883 | 197 |