Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 5. C2×#14273663 | C4 | semidirect |
| 8. C22⋊(C59⋊C16) | C4 | semidirect |
| 125. C59 | #7260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C59⋊C16) | 2 |
| #21424134 | 2 |
| C59×#1735 | 2 |
| #7260 | 59 |