Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #21432691 | C2 | semidirect |
| 3. #21425833 | C2 | semidirect |
| 4. C2×#16837213 | C2 | semidirect |
| 5. C59×#3407 | C2 | semidirect |
| 7. #16838219 | C4 | semidirect |
| 9. #16838207 | C4 | semidirect |
| 14. #16837440 | C22 | semidirect |
| 15. C2×#14273659 | C22 | semidirect |
| 16. #16837213 | C22 | semidirect |
| 17. #16837213 | C22 | semidirect |
| 20. C2×M32×C59 | C22 | semidirect |
| 31. #14273749 | C2×C4 | semidirect |
| 33. C2×Dic236 | C2×C4 | semidirect |
| 35. C2×D472 | C2×C4 | semidirect |
| 123. #3407 | D59 | semidirect |
| 140. C2×M32 | C2×D59 | semidirect |
| 146. C59 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438870 | 2 |
| #21432691 | 2 |
| #21425833 | 2 |
| C2×#16837213 | 2 |
| C59×#3407 | 2 |
| #33388 | 59 |