Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#20263348 | C2 | semidirect |
| 2. C2×#20263346 | C2 | semidirect |
| 3. #27161625 | C2 | semidirect |
| 4. #27161464 | C2 | semidirect |
| 5. #27161462 | C2 | semidirect |
| 6. #27161460 | C2 | semidirect |
| 7. #27161457 | C2 | semidirect |
| 8. #27161454 | C2 | semidirect |
| 9. #27161450 | C2 | semidirect |
| 10. C2×C8×Dic197 | C2 | semidirect |
| 11. C2×#135×C197 | C2 | semidirect |
| 55. C2×#13096802 | D4 | semidirect |
| 74. C2×C8×C197 | D4 | semidirect |
| 119. Dic197 | #135 | semidirect |
| 125. C197 | #3147 | semidirect |
| 129. C2×#135 | D197 | semidirect |
| 194. C2×C8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263348 | 2 |
| C2×#20263346 | 2 |
| #27161625 | 2 |
| #27161464 | 2 |
| #27161462 | 2 |
| #27161460 | 2 |
| #27161457 | 2 |
| #27161454 | 2 |
| #27161450 | 2 |
| C2×C8×Dic197 | 2 |
| C2×#135×C197 | 2 |
| #3147 | 197 |