Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
584 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21425498 | C2 | semidirect |
| 4. #21425497 | C2 | semidirect |
| 5. #21425496 | C2 | semidirect |
| 7. C59×#2070 | C2 | semidirect |
| 105. #2070 | D59 | semidirect |
| 123. C59 | #32876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425613 | 2 |
| #21425611 | 2 |
| #21425498 | 2 |
| #21425497 | 2 |
| #21425496 | 2 |
| #21424018 | 2 |
| C59×#2070 | 2 |
| #32876 | 59 |