Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #27161417 | C2 | semidirect |
| 3. #27161412 | C2 | semidirect |
| 4. #27161407 | C2 | semidirect |
| 5. #27161119 | C2 | semidirect |
| 6. #27161088 | C2 | semidirect |
| 18. #20263259 | C22 | semidirect |
| 19. #20263257 | C22 | semidirect |
| 20. #20263250 | C22 | semidirect |
| 21. #20263250 | C22 | semidirect |
| 116. C197 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263285 | 2 |
| #27161417 | 2 |
| #27161412 | 2 |
| #27161407 | 2 |
| #27161119 | 2 |
| #27161088 | 2 |
| #27161043 | 2 |
| C2×C22⋊Q8×C197 | 2 |
| #3095 | 197 |