Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426233 | C2 | semidirect |
| 3. #21423688 | C2 | semidirect |
| 4. #21422166 | C2 | semidirect |
| 5. #21422152 | C2 | semidirect |
| 6. #21422141 | C2 | semidirect |
| 7. C59×#1589 | C2 | semidirect |
| 94. C8×C59 | D16 | semidirect |
| 115. #1589 | D59 | semidirect |
| 139. C59 | #12483 | semidirect |
| 211. C8 | #14273668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426233 | 2 |
| #21426131 | 2 |
| #21423688 | 2 |
| #21422166 | 2 |
| #21422152 | 2 |
| #21422141 | 2 |
| C59×#1589 | 2 |
| #12483 | 59 |