Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
800 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 800 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. #21425074 | C2 | semidirect |
| 2. #21424925 | C2 | semidirect |
| 3. #21422834 | C2 | semidirect |
| 4. #21422831 | C2 | semidirect |
| 14. C59×#562 | C4 | semidirect |
| 147. #562 | Dic59 | semidirect |
| 163. C59 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425074 | 2 |
| #21424925 | 2 |
| #21422834 | 2 |
| #21422831 | 2 |
| C59×#3548 | 2 |
| #8532 | 59 |