Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#20263357 | C2 | semidirect |
| 3. #27161235 | C2 | semidirect |
| 4. #27161218 | C2 | semidirect |
| 5. #27161088 | C2 | semidirect |
| 6. #27161043 | C2 | semidirect |
| 7. C23×Q8×C197 | C2 | semidirect |
| 10. C2×#15691348 | C22 | semidirect |
| 11. C2×#15691345 | C22 | semidirect |
| 19. #20263250 | C22 | semidirect |
| 51. C2×Q8×C197 | D4 | semidirect |
| 93. C22×C197 | #137 | semidirect |
| 108. C197 | #3004 | semidirect |
| 110. C23×Q8 | D197 | semidirect |
| 146. C2×Q8 | C22⋊D197 | semidirect |
| 204. C22 | #20263357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| #27161590 | 2 |
| #27161235 | 2 |
| #27161218 | 2 |
| #27161088 | 2 |
| #27161043 | 2 |
| C23×Q8×C197 | 2 |
| #3004 | 197 |