Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20263357 | C2 | semidirect |
| 3. #27161261 | C2 | direct (N × H) |
| 4. C2×#20263254 | C2 | semidirect |
| 5. C2×#20263245 | C2 | semidirect |
| 6. C2×C4⋊Q8×C197 | C2 | semidirect |
| 15. #20263357 | C22 | semidirect |
| 19. #20263254 | C22 | semidirect |
| 20. #20263245 | C22 | semidirect |
| 24. C4⋊Q8×C197 | C22 | semidirect |
| 109. C2×C197 | #456 | semidirect |
| 112. C197 | C2×#456 | semidirect |
| 116. C2×C4⋊Q8 | D197 | semidirect |
| 135. C4⋊Q8 | C2×D197 | semidirect |
| 223. C2 | #27161261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263374 | 2 |
| C2×#20263357 | 2 |
| #27161261 | 2 |
| C2×#20263254 | 2 |
| C2×#20263245 | 2 |
| C2×C4⋊Q8×C197 | 2 |
| C2×#456 | 197 |