Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. #21424249 | C2 | semidirect |
| 4. #21422608 | C2 | semidirect |
| 6. #21421965 | C2 | semidirect |
| 7. C59×#1552 | C2 | semidirect |
| 155. #1552 | D59 | semidirect |
| 184. C59 | #10514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435408 | 2 |
| #21424249 | 2 |
| #21422789 | 2 |
| #21422608 | 2 |
| #21422605 | 2 |
| #21421965 | 2 |
| C59×#1552 | 2 |
| #10514 | 59 |