Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 2. C2×#16837226 | C2 | semidirect |
| 5. #21424877 | C2 | semidirect |
| 6. #21422181 | C2 | semidirect |
| 7. C59×#1388 | C2 | semidirect |
| 18. #16837217 | C4 | semidirect |
| 19. #16837214 | C4 | semidirect |
| 145. #1388 | D59 | semidirect |
| 169. C59 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433012 | 2 |
| C2×#16837226 | 2 |
| #21425843 | 2 |
| C2×#16837213 | 2 |
| #21424877 | 2 |
| #21422181 | 2 |
| C59×#1388 | 2 |
| #12952 | 59 |