Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 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. C22×Q8×D197 | C2 | semidirect |
| 2. C2×#20263356 | C2 | semidirect |
| 4. #27161233 | C2 | semidirect |
| 5. #27161216 | C2 | semidirect |
| 6. #27161089 | C2 | semidirect |
| 7. #27161088 | C2 | semidirect |
| 8. #27161042 | C2 | semidirect |
| 9. C2×#137×C197 | C2 | semidirect |
| 19. C2×#15691348 | C22 | semidirect |
| 20. C2×#15691346 | C22 | semidirect |
| 28. #20263251 | C22 | semidirect |
| 29. #20263250 | C22 | semidirect |
| 34. C2×Q16×C197 | C22 | semidirect |
| 35. C2×SD16×C197 | C22 | semidirect |
| 42. C2×Dic394 | D4 | semidirect |
| 70. C2×Q8×C197 | D4 | semidirect |
| 127. C2×D197 | #137 | semidirect |
| 141. C197 | #3004 | semidirect |
| 145. C2×#137 | D197 | semidirect |
| 165. C2×Q16 | C2×D197 | semidirect |
| 167. C2×SD16 | C2×D197 | semidirect |
| 193. C2×Q8 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D197 | 2 |
| C2×#20263356 | 2 |
| #27161586 | 2 |
| #27161233 | 2 |
| #27161216 | 2 |
| #27161089 | 2 |
| #27161088 | 2 |
| #27161042 | 2 |
| C2×#137×C197 | 2 |
| #3004 | 197 |