Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16837225 | C2 | semidirect |
| 5. #21424876 | C2 | semidirect |
| 6. #21422208 | C2 | semidirect |
| 7. C59×#1378 | C2 | semidirect |
| 18. #16837219 | C4 | semidirect |
| 19. #16837216 | C4 | semidirect |
| 146. #1378 | 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 |
|---|---|
| #21433014 | 2 |
| C2×#16837225 | 2 |
| #21425846 | 2 |
| C2×#16837213 | 2 |
| #21424876 | 2 |
| #21422208 | 2 |
| C59×#1378 | 2 |
| #12952 | 59 |