Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 2. #21422859 | C2 | semidirect |
| 3. #21422058 | C2 | semidirect |
| 4. C59×#2162 | C2 | semidirect |
| 14. #16837155 | C22 | semidirect |
| 19. C4×C16×C59 | C22 | semidirect |
| 122. #2162 | D59 | semidirect |
| 142. C4×C16 | C2×D59 | semidirect |
| 145. C59 | #11661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D472 | 2 |
| #21422859 | 2 |
| #21422058 | 2 |
| C59×#2162 | 2 |
| #11661 | 59 |