Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic394 | C2 | semidirect |
| 2. #27161412 | C2 | semidirect |
| 4. #27161383 | C2 | semidirect |
| 5. #27161298 | C2 | semidirect |
| 6. #27161234 | C2 | semidirect |
| 8. #27161184 | C2 | semidirect |
| 9. #27161179 | C2 | semidirect |
| 10. #27161136 | C2 | semidirect |
| 131. C197 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic394 | 2 |
| #27161412 | 2 |
| #27161395 | 2 |
| #27161383 | 2 |
| #27161298 | 2 |
| #27161234 | 2 |
| #27161217 | 2 |
| #27161184 | 2 |
| #27161179 | 2 |
| #27161136 | 2 |
| #529×C197 | 2 |
| #3117 | 197 |