Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16837224 | C2 | semidirect |
| 4. #21424849 | C2 | semidirect |
| 5. #21422203 | C2 | semidirect |
| 6. #21422176 | C2 | semidirect |
| 15. #16837203 | C4 | semidirect |
| 31. C2×C59⋊C16 | C2×C4 | semidirect |
| 34. #14273661 | C2×C4 | semidirect |
| 168. C59 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837224 | 2 |
| C2×#16837215 | 2 |
| #21425812 | 2 |
| #21424849 | 2 |
| #21422203 | 2 |
| #21422176 | 2 |
| C2×C59×#442 | 2 |
| #12956 | 59 |