Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
598 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21434214 | C2 | semidirect |
| 3. #21429959 | C2 | semidirect |
| 4. #21422719 | C2 | semidirect |
| 5. #21422542 | C2 | semidirect |
| 6. #21421960 | C2 | semidirect |
| 7. C59×#1514 | C2 | semidirect |
| 211. #1514 | D59 | semidirect |
| 245. C59 | #10020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434564 | 2 |
| #21434214 | 2 |
| #21429959 | 2 |
| #21422719 | 2 |
| #21422542 | 2 |
| #21421960 | 2 |
| C59×#1514 | 2 |
| #10020 | 59 |