Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
710 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 199 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. #21424903 | C2 | semidirect |
| 2. #21424253 | C2 | semidirect |
| 3. C2×#16837123 | C2 | semidirect |
| 13. C59×#493 | C4 | semidirect |
| 76. C8×C59 | #102 | semidirect |
| 105. #493 | Dic59 | semidirect |
| 112. C59 | #9837 | semidirect |
| 175. C8 | #14273648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424903 | 2 |
| #21424253 | 2 |
| C2×#16837123 | 2 |
| C2×C59×#493 | 2 |
| #9837 | 59 |