Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 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. #27161636 | C2 | semidirect |
| 2. #27161379 | C2 | semidirect |
| 3. #27161369 | C2 | semidirect |
| 4. #27161359 | C2 | semidirect |
| 5. #27161119 | C2 | semidirect |
| 6. #27161103 | C2 | semidirect |
| 10. #20263326 | C22 | semidirect |
| 11. #20263326 | C22 | semidirect |
| 12. #20263318 | C22 | semidirect |
| 18. #20263259 | C22 | semidirect |
| 19. #20263257 | C22 | semidirect |
| 20. C4⋊#13096802 | C22 | semidirect |
| 21. C4⋊#13096802 | C22 | semidirect |
| 48. C2×D4×C197 | Q8 | semidirect |
| 115. C197 | #3077 | semidirect |
| 154. C2×D4 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| #27161379 | 2 |
| #27161369 | 2 |
| #27161359 | 2 |
| #27161119 | 2 |
| #27161103 | 2 |
| #27161084 | 2 |
| C2×C4×D4×C197 | 2 |
| #3077 | 197 |