Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
366 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #21422211 | C2 | semidirect |
| 5. #21422193 | C2 | semidirect |
| 6. #21422191 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 12. #16837449 | C4 | semidirect |
| 136. #1389 | D59 | semidirect |
| 158. C59 | #12877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432704 | 2 |
| #21425711 | 2 |
| #21424139 | 2 |
| #21422211 | 2 |
| #21422193 | 2 |
| #21422191 | 2 |
| C59×#1389 | 2 |
| #12877 | 59 |