Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
474 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16837195 | C2 | semidirect |
| 3. #21422260 | C2 | semidirect |
| 4. #21422258 | C2 | semidirect |
| 5. C2×C59×#353 | C2 | semidirect |
| 8. #16837952 | C4 | semidirect |
| 11. #16837778 | C4 | semidirect |
| 13. #16837774 | C4 | semidirect |
| 16. C4×#11745664 | C4 | semidirect |
| 37. #14273727 | C2×C4 | semidirect |
| 38. #14273724 | C2×C4 | semidirect |
| 46. C4×C59⋊C8 | C2×C4 | semidirect |
| 47. C4×C59⋊C8 | C2×C4 | semidirect |
| 184. C2×#353 | D59 | semidirect |
| 213. C59 | #13584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434546 | 2 |
| C2×#16837195 | 2 |
| #21422260 | 2 |
| #21422258 | 2 |
| C2×C59×#353 | 2 |
| #13584 | 59 |