Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 648 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 |
|---|---|---|
| 2. #21422723 | C2 | semidirect |
| 3. #21422632 | C2 | semidirect |
| 4. #21422557 | C2 | semidirect |
| 5. C59×#1991 | C2 | semidirect |
| 6. C59⋊#564 | C4 | semidirect |
| 7. #16838156 | C4 | semidirect |
| 8. #16838150 | C4 | semidirect |
| 176. #1991 | D59 | semidirect |
| 205. C59 | #8529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438552 | 2 |
| #21422723 | 2 |
| #21422632 | 2 |
| #21422557 | 2 |
| C59×#1991 | 2 |
| #8529 | 59 |