Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 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. #21425868 | C2 | semidirect |
| 5. #21424887 | C2 | semidirect |
| 6. #21422181 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 19. #16837214 | C4 | semidirect |
| 38. #14273667 | C2×C4 | semidirect |
| 53. #108×C59 | C2×C4 | semidirect |
| 138. #1389 | D59 | semidirect |
| 161. C59 | #12953 | semidirect |
| 188. #108 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432947 | 2 |
| #21425868 | 2 |
| C2×#16837216 | 2 |
| C2×#16837214 | 2 |
| #21424887 | 2 |
| #21422181 | 2 |
| C59×#1389 | 2 |
| #12953 | 59 |