Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
888 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. #21424925 | C2 | semidirect |
| 2. #21422831 | C2 | semidirect |
| 4. #16837426 | C22 | semidirect |
| 6. C42×Dic59 | C22 | semidirect |
| 9. C59×H(3,𝔽4) | C4 | semidirect |
| 90. H(3,𝔽4) | Dic59 | semidirect |
| 100. C59 | #8530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424925 | 2 |
| #21422831 | 2 |
| C59×#3549 | 2 |
| #8530 | 59 |