Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
440 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 143 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. #27161632 | C2 | semidirect |
| 3. #27161381 | C2 | semidirect |
| 4. #27161377 | C2 | semidirect |
| 5. #27161367 | C2 | semidirect |
| 6. #27161357 | C2 | semidirect |
| 7. #27161122 | C2 | semidirect |
| 8. #27161121 | C2 | semidirect |
| 9. #27161102 | C2 | semidirect |
| 14. #20263325 | C22 | semidirect |
| 15. #20263325 | C22 | semidirect |
| 16. #20263317 | C22 | semidirect |
| 17. #20263317 | C22 | semidirect |
| 30. #20263260 | C22 | semidirect |
| 31. #20263259 | C22 | semidirect |
| 32. #20263258 | C22 | semidirect |
| 33. #20263257 | C22 | semidirect |
| 34. #20263255 | C22 | semidirect |
| 35. #20263255 | C22 | semidirect |
| 74. C2×D4×C197 | Q8 | semidirect |
| 138. C197 | #3077 | semidirect |
| 187. C2×D4 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161632 | 2 |
| C2×D4×Dic197 | 2 |
| #27161381 | 2 |
| #27161377 | 2 |
| #27161367 | 2 |
| #27161357 | 2 |
| #27161122 | 2 |
| #27161121 | 2 |
| #27161102 | 2 |
| #27161084 | 2 |
| #418×C197 | 2 |
| #3077 | 197 |