Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161707 | C2 | semidirect |
| 3. #27161381 | C2 | semidirect |
| 4. #27161377 | C2 | semidirect |
| 5. #27161367 | C2 | semidirect |
| 6. #27161357 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161115 | C2 | semidirect |
| 9. #27161107 | C2 | semidirect |
| 14. #20263325 | C22 | semidirect |
| 16. #20263317 | C22 | semidirect |
| 26. #20263260 | C22 | semidirect |
| 27. #20263259 | C22 | semidirect |
| 28. #20263259 | C22 | semidirect |
| 29. #20263258 | C22 | semidirect |
| 30. #20263257 | C22 | semidirect |
| 31. #20263257 | C22 | semidirect |
| 32. #20263255 | C22 | semidirect |
| 33. #20263255 | C22 | semidirect |
| 66. C2×D4×C197 | Q8 | semidirect |
| 124. C197 | #3081 | semidirect |
| 170. C2×D4 | Dic394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161707 | 2 |
| #27161554 | 2 |
| #27161381 | 2 |
| #27161377 | 2 |
| #27161367 | 2 |
| #27161357 | 2 |
| #27161121 | 2 |
| #27161115 | 2 |
| #27161107 | 2 |
| C2×#20263247 | 2 |
| #418×C197 | 2 |
| #3081 | 197 |