Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21434618 | C2 | semidirect |
| 5. #21422659 | C2 | semidirect |
| 6. #21421940 | C2 | semidirect |
| 7. C59×#1518 | C2 | semidirect |
| 121. C2×C59⋊C8 | SD16 | semidirect |
| 186. #1518 | D59 | semidirect |
| 217. C59 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435039 | 2 |
| #21435034 | 2 |
| #21434618 | 2 |
| #21424919 | 2 |
| #21422659 | 2 |
| #21421940 | 2 |
| C59×#1518 | 2 |
| #10220 | 59 |