Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
656 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21424658 | C2 | semidirect |
| 4. #21423967 | C2 | semidirect |
| 6. #21423783 | C2 | semidirect |
| 7. C59×#1840 | C2 | semidirect |
| 116. #1840 | D59 | semidirect |
| 141. C59 | #21670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427394 | 2 |
| #21424707 | 2 |
| #21424658 | 2 |
| #21423967 | 2 |
| #21423876 | 2 |
| #21423783 | 2 |
| C59×#1840 | 2 |
| #21670 | 59 |