Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
652 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×#14273642 | C2 | semidirect |
| 3. #21422094 | C2 | semidirect |
| 4. C59×#1465 | C2 | semidirect |
| 5. C2×#14273724 | C4 | semidirect |
| 10. #16837311 | C4 | semidirect |
| 13. C4×C4⋊Dic59 | C4 | semidirect |
| 180. #1465 | D59 | semidirect |
| 205. C59 | #11776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429042 | 2 |
| C4×#14273642 | 2 |
| #21422094 | 2 |
| C59×#1465 | 2 |
| #11776 | 59 |