Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#16837222 | C2 | semidirect |
| 5. #21424259 | C2 | semidirect |
| 6. #21422206 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 12. #16837518 | C4 | semidirect |
| 157. #1387 | D59 | semidirect |
| 182. C59 | #12820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837518 | 2 |
| C2×#16837222 | 2 |
| #21425809 | 2 |
| #21425806 | 2 |
| #21424259 | 2 |
| #21422206 | 2 |
| C59×#1387 | 2 |
| #12820 | 59 |