Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#16837224 | C2 | semidirect |
| 4. #21424822 | C2 | semidirect |
| 5. #21422195 | C2 | semidirect |
| 6. #21422177 | C2 | semidirect |
| 18. #16837212 | C4 | semidirect |
| 72. Q16×C59 | C4⋊C4 | semidirect |
| 76. D8×C59 | C4⋊C4 | semidirect |
| 180. C59 | #12950 | semidirect |
| 229. Q16 | Dic59⋊C4 | semidirect |
| 233. D8 | Dic59⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837519 | 2 |
| C2×#16837224 | 2 |
| C2×#16837212 | 2 |
| #21424822 | 2 |
| #21422195 | 2 |
| #21422177 | 2 |
| C2×C59×#360 | 2 |
| #12950 | 59 |