Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21424233 | C2 | semidirect |
| 3. #21422551 | C2 | semidirect |
| 6. C2×#16837124 | C2 | semidirect |
| 7. C59×#1493 | C2 | semidirect |
| 156. #1493 | D59 | semidirect |
| 184. C59 | #9863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434421 | 2 |
| #21424233 | 2 |
| #21422551 | 2 |
| #21422548 | 2 |
| #21422546 | 2 |
| C2×#16837124 | 2 |
| C59×#1493 | 2 |
| #9863 | 59 |