Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #27161630 | C2 | semidirect |
| 2. #27161627 | C2 | semidirect |
| 3. #27161482 | C2 | semidirect |
| 4. #27161455 | C2 | semidirect |
| 5. #27161426 | C2 | semidirect |
| 6. #27161314 | C2 | semidirect |
| 7. #27161159 | C2 | semidirect |
| 8. C4×C8×D197 | C2 | semidirect |
| 9. #486×C197 | C2 | semidirect |
| 84. C4×D197 | D8 | semidirect |
| 85. #13096802 | #41 | semidirect |
| 120. C197 | #3169 | semidirect |
| 127. #486 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161630 | 2 |
| #27161627 | 2 |
| #27161482 | 2 |
| #27161455 | 2 |
| #27161426 | 2 |
| #27161314 | 2 |
| #27161159 | 2 |
| C4×C8×D197 | 2 |
| #486×C197 | 2 |
| #3169 | 197 |