Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16837225 | C2 | semidirect |
| 5. #21423993 | C2 | semidirect |
| 6. #21422205 | C2 | semidirect |
| 7. C59×#1375 | C2 | semidirect |
| 17. #16837207 | C4 | semidirect |
| 18. #16837204 | C4 | semidirect |
| 149. #1375 | D59 | semidirect |
| 171. C59 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837225 | 2 |
| C2×#16837213 | 2 |
| #21425809 | 2 |
| #21424989 | 2 |
| #21423993 | 2 |
| #21422205 | 2 |
| C59×#1375 | 2 |
| #13143 | 59 |