Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #27161120 | C2 | semidirect |
| 4. #27161118 | C2 | semidirect |
| 5. #27161117 | C2 | semidirect |
| 6. #27161115 | C2 | semidirect |
| 7. #427×C197 | C2 | semidirect |
| 9. C2×#15691341 | C4 | semidirect |
| 20. #20263260 | C22 | semidirect |
| 21. #20263259 | C22 | semidirect |
| 22. #20263258 | C22 | semidirect |
| 23. #20263257 | C22 | semidirect |
| 26. #107×C197 | C22 | semidirect |
| 27. #106×C197 | C22 | semidirect |
| 35. #15691341 | C2×C4 | semidirect |
| 36. #15691341 | C2×C4 | semidirect |
| 37. C2×#13096802 | C2×C4 | semidirect |
| 46. C2×C8×C197 | C2×C4 | semidirect |
| 87. C197 | #2911 | semidirect |
| 95. #427 | D197 | semidirect |
| 112. #107 | C2×D197 | semidirect |
| 115. #106 | C2×D197 | semidirect |
| 128. C2×C8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691341 | 2 |
| #117×D197 | 2 |
| #27161120 | 2 |
| #27161118 | 2 |
| #27161117 | 2 |
| #27161115 | 2 |
| #427×C197 | 2 |
| #2911 | 197 |