Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
392 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21422204 | C2 | semidirect |
| 5. #21422196 | C2 | semidirect |
| 6. #21422195 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 12. #16837449 | C4 | semidirect |
| 149. #1387 | D59 | semidirect |
| 172. C59 | #12875 | 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 |
| #21424130 | 2 |
| #21422204 | 2 |
| #21422196 | 2 |
| #21422195 | 2 |
| C59×#1387 | 2 |
| #12875 | 59 |