Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425861 | C2 | semidirect |
| 5. #21422183 | C2 | semidirect |
| 6. #21422180 | C2 | semidirect |
| 7. C2×C59×#347 | C2 | semidirect |
| 137. C2×#347 | D59 | semidirect |
| 161. C59 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425861 | 2 |
| #21425725 | 2 |
| #21425716 | 2 |
| #21423940 | 2 |
| #21422183 | 2 |
| #21422180 | 2 |
| C2×C59×#347 | 2 |
| #13127 | 59 |