Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
470 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21437199 | C2 | semidirect |
| 3. #21425831 | C2 | semidirect |
| 4. #21422201 | C2 | semidirect |
| 5. C59×#1812 | C2 | semidirect |
| 11. #16837660 | C4 | semidirect |
| 12. #16837655 | C4 | semidirect |
| 35. #14273667 | D4 | semidirect |
| 137. #1812 | D59 | semidirect |
| 159. C59 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437199 | 2 |
| #21433758 | 2 |
| #21425831 | 2 |
| #21422201 | 2 |
| C59×#1812 | 2 |
| #13077 | 59 |