Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
370 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #21422207 | C2 | semidirect |
| 5. #21422200 | C2 | semidirect |
| 6. #21422199 | C2 | semidirect |
| 7. C59×#1388 | C2 | semidirect |
| 138. #1388 | D59 | semidirect |
| 160. C59 | #12876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837449 | 2 |
| C2×#16837183 | 2 |
| #21424135 | 2 |
| #21422207 | 2 |
| #21422200 | 2 |
| #21422199 | 2 |
| C59×#1388 | 2 |
| #12876 | 59 |