Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #21435288 | C2 | semidirect |
| 3. #21429262 | C2 | semidirect |
| 4. #21425015 | C2 | semidirect |
| 5. #21422697 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1490 | C2 | semidirect |
| 215. #1490 | D59 | semidirect |
| 249. C59 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435288 | 2 |
| #21434187 | 2 |
| #21429262 | 2 |
| #21425015 | 2 |
| #21422697 | 2 |
| #21421953 | 2 |
| C59×#1490 | 2 |
| #10005 | 59 |