Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
890 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 159 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. #21425832 | C2 | semidirect |
| 2. #21425803 | C2 | semidirect |
| 3. #21425710 | C2 | semidirect |
| 4. #21424142 | C2 | semidirect |
| 6. C2×#14273667 | C22 | semidirect |
| 7. C22×C59⋊C16 | C22 | semidirect |
| 8. #16837440 | C22 | semidirect |
| 20. C59×#575 | C4 | semidirect |
| 178. #575 | Dic59 | semidirect |
| 191. C59 | #12745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425832 | 2 |
| #21425803 | 2 |
| #21425710 | 2 |
| #21424142 | 2 |
| C59×#3584 | 2 |
| #12745 | 59 |