Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21426698 | C2 | semidirect |
| 4. C2×#16837127 | C2 | semidirect |
| 5. #21421964 | C2 | semidirect |
| 6. #21421963 | C2 | semidirect |
| 11. #16837333 | C4 | semidirect |
| 13. #16837316 | C4 | semidirect |
| 250. C59 | #9206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429840 | 2 |
| #21426698 | 2 |
| #21422664 | 2 |
| C2×#16837127 | 2 |
| #21421964 | 2 |
| #21421963 | 2 |
| C59×#1519 | 2 |
| #9206 | 59 |