Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20263347 | C2 | semidirect |
| 2. #27161751 | C2 | semidirect |
| 3. #27161733 | C2 | semidirect |
| 4. #27161452 | C2 | semidirect |
| 5. #27161309 | C2 | semidirect |
| 6. #27161289 | C2 | semidirect |
| 7. #27161274 | C2 | semidirect |
| 8. #27161244 | C2 | semidirect |
| 9. #27161225 | C2 | semidirect |
| 10. C8×D788 | C2 | semidirect |
| 11. C4×SD16×C197 | C2 | semidirect |
| 73. SD16×C197 | D4 | semidirect |
| 129. C4×C197 | #135 | semidirect |
| 140. C197 | #3284 | semidirect |
| 151. C4×SD16 | D197 | semidirect |
| 204. SD16 | D788 | semidirect |
| 272. C4 | #20263347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263347 | 2 |
| #27161751 | 2 |
| #27161733 | 2 |
| #27161452 | 2 |
| #27161309 | 2 |
| #27161289 | 2 |
| #27161274 | 2 |
| #27161244 | 2 |
| #27161225 | 2 |
| C8×D788 | 2 |
| C4×SD16×C197 | 2 |
| #3284 | 197 |