Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 398 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. #21422206 | C2 | semidirect |
| 5. #21422205 | C2 | semidirect |
| 6. #21422204 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 147. #1387 | D59 | semidirect |
| 168. C59 | #12872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837439 | 2 |
| #21425706 | 2 |
| #21424131 | 2 |
| #21422206 | 2 |
| #21422205 | 2 |
| #21422204 | 2 |
| C59×#1387 | 2 |
| #12872 | 59 |