Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161629 | C2 | semidirect |
| 2. #27161482 | C2 | semidirect |
| 3. #27161455 | C2 | semidirect |
| 4. #27161427 | C2 | semidirect |
| 5. #27161425 | C2 | semidirect |
| 6. #27161313 | C2 | semidirect |
| 7. C4×#15691343 | C2 | semidirect |
| 8. C2×C4×#13096802 | C2 | semidirect |
| 9. #532×C197 | C2 | semidirect |
| 77. #13096802 | #41 | semidirect |
| 89. C2×C4×C197 | D8 | semidirect |
| 120. C197 | #3169 | semidirect |
| 123. #532 | D197 | semidirect |
| 208. C2×C4 | #15691343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161629 | 2 |
| #27161482 | 2 |
| #27161455 | 2 |
| #27161427 | 2 |
| #27161425 | 2 |
| #27161313 | 2 |
| C4×#15691343 | 2 |
| C2×C4×#13096802 | 2 |
| #532×C197 | 2 |
| #3169 | 197 |