Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16837226 | C2 | semidirect |
| 5. #21423995 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 17. #16837205 | C4 | semidirect |
| 18. #16837202 | C4 | semidirect |
| 148. #1387 | 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×#16837226 | 2 |
| C2×#16837213 | 2 |
| #21425806 | 2 |
| #21424987 | 2 |
| #21423995 | 2 |
| #21422175 | 2 |
| C59×#1387 | 2 |
| #13143 | 59 |