Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 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 |
|---|---|---|
| 2. C2×#20263355 | C2 | semidirect |
| 3. C22⋊Q8×D197 | C2 | semidirect |
| 4. #27161242 | C2 | semidirect |
| 5. #27161238 | C2 | semidirect |
| 6. #27161237 | C2 | semidirect |
| 7. #27161234 | C2 | semidirect |
| 8. #27161230 | C2 | semidirect |
| 9. #27161077 | C2 | semidirect |
| 10. #27161041 | C2 | semidirect |
| 11. #450×C197 | C2 | semidirect |
| 18. C2×Q8×D197 | C22 | semidirect |
| 23. C2×Dic788 | C22 | semidirect |
| 24. C2×#15691348 | C22 | semidirect |
| 25. C2×#15691346 | C22 | semidirect |
| 26. C2×#15691341 | C22 | semidirect |
| 27. #20263306 | C22 | semidirect |
| 31. #20263302 | C22 | semidirect |
| 33. C4⋊C4×D197 | C22 | semidirect |
| 35. #20263251 | C22 | semidirect |
| 36. #20263249 | C22 | semidirect |
| 37. #20263247 | C22 | semidirect |
| 39. #20263238 | C22 | semidirect |
| 41. C2×SD16×C197 | C22 | semidirect |
| 43. #102×C197 | C22 | semidirect |
| 146. C22×C197 | #137 | semidirect |
| 171. C197 | #3007 | semidirect |
| 181. #450 | D197 | semidirect |
| 199. C2×SD16 | C2×D197 | semidirect |
| 213. #102 | C2×D197 | semidirect |
| 325. C22 | #20263355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691357 | 2 |
| C2×#20263355 | 2 |
| C22⋊Q8×D197 | 2 |
| #27161242 | 2 |
| #27161238 | 2 |
| #27161237 | 2 |
| #27161234 | 2 |
| #27161230 | 2 |
| #27161077 | 2 |
| #27161041 | 2 |
| #450×C197 | 2 |
| #3007 | 197 |