Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
672 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 3. #21425770 | C2 | semidirect |
| 4. #21425751 | C2 | semidirect |
| 5. #21422226 | C2 | semidirect |
| 6. #21422216 | C2 | semidirect |
| 8. C2×#14273757 | C4 | semidirect |
| 9. C22×#11745670 | C4 | semidirect |
| 16. #16837407 | C4 | semidirect |
| 17. #16837398 | C4 | semidirect |
| 31. C22×Dic118 | C2×C4 | semidirect |
| 38. C2×#11745664 | C2×C4 | semidirect |
| 39. C22×C59⋊C8 | C2×C4 | semidirect |
| 50. #14273686 | C2×C4 | semidirect |
| 282. C59 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433373 | 2 |
| #21432557 | 2 |
| #21425770 | 2 |
| #21425751 | 2 |
| #21422226 | 2 |
| #21422216 | 2 |
| C59×#1795 | 2 |
| #13100 | 59 |