Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
580 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 580 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 |
|---|---|---|
| 3. #21424379 | C2 | semidirect |
| 4. #21422213 | C2 | semidirect |
| 19. C59×#353 | C4 | semidirect |
| 47. #99×C59 | C2×C4 | semidirect |
| 59. C2×D4×C59 | C4⋊C4 | semidirect |
| 77. C42×C59 | C4⋊C4 | semidirect |
| 178. #353 | Dic59 | semidirect |
| 181. C59 | #12966 | semidirect |
| 204. #99 | C2×Dic59 | semidirect |
| 221. C2×D4 | C4⋊Dic59 | semidirect |
| 251. C42 | C4⋊Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427273 | 2 |
| #21424495 | 2 |
| #21424379 | 2 |
| #21422213 | 2 |
| C2×C59×#353 | 2 |
| #12966 | 59 |