Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21425037 | C2 | semidirect |
| 5. #21421991 | C2 | semidirect |
| 6. #21421940 | C2 | semidirect |
| 7. C59×#1487 | C2 | semidirect |
| 117. C2×C59⋊C8 | SD16 | semidirect |
| 184. #1487 | D59 | semidirect |
| 214. C59 | #9047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434127 | 2 |
| #21432813 | 2 |
| #21425037 | 2 |
| #21422743 | 2 |
| #21421991 | 2 |
| #21421940 | 2 |
| C59×#1487 | 2 |
| #9047 | 59 |