Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
194 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 194 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. #21422297 | C2 | semidirect |
| 4. #21422295 | C2 | semidirect |
| 7. #16837236 | C4 | semidirect |
| 20. C59⋊C32 | C2×C4 | semidirect |
| 86. C59 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837236 | 2 |
| #21425880 | 2 |
| #21422297 | 2 |
| #21422295 | 2 |
| C2×C59×#366 | 2 |
| #13634 | 59 |