Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#16837215 | C2 | semidirect |
| 2. #21425832 | C2 | semidirect |
| 3. #21425824 | C2 | semidirect |
| 4. #21425812 | C2 | semidirect |
| 5. #21425701 | C2 | semidirect |
| 6. #21424220 | C2 | semidirect |
| 24. C59×#495 | C4 | semidirect |
| 25. C59×#493 | C4 | semidirect |
| 32. #14273667 | D4 | semidirect |
| 34. C2×C59⋊C16 | D4 | semidirect |
| 189. #495 | Dic59 | semidirect |
| 190. #493 | Dic59 | semidirect |
| 201. C59 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837215 | 2 |
| #21425832 | 2 |
| #21425824 | 2 |
| #21425812 | 2 |
| #21425701 | 2 |
| #21424220 | 2 |
| C59×#3155 | 2 |
| #13215 | 59 |