Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
666 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21432575 | C2 | semidirect |
| 3. #21425787 | C2 | semidirect |
| 4. #21425745 | C2 | semidirect |
| 5. #21422224 | C2 | semidirect |
| 6. #21422218 | C2 | semidirect |
| 7. C59×#1795 | C2 | semidirect |
| 8. C2×#14273752 | C4 | semidirect |
| 9. C22×#11745669 | C4 | semidirect |
| 16. #16837407 | C4 | semidirect |
| 17. #16837398 | C4 | semidirect |
| 251. #1795 | D59 | semidirect |
| 286. C59 | #13099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433364 | 2 |
| #21432575 | 2 |
| #21425787 | 2 |
| #21425745 | 2 |
| #21422224 | 2 |
| #21422218 | 2 |
| C59×#1795 | 2 |
| #13099 | 59 |