Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
894 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21425717 | C2 | semidirect |
| 3. #21425716 | C2 | semidirect |
| 4. #21425709 | C2 | semidirect |
| 5. C59×#2113 | C2 | semidirect |
| 14. C2×#14273667 | C22 | semidirect |
| 19. C2×M32×C59 | C22 | semidirect |
| 20. C22×C16×C59 | C22 | semidirect |
| 164. #2113 | D59 | semidirect |
| 180. C2×M32 | C2×D59 | semidirect |
| 181. C22×C16 | C2×D59 | semidirect |
| 186. C59 | #12684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438807 | 2 |
| #21425717 | 2 |
| #21425716 | 2 |
| #21425709 | 2 |
| C59×#2113 | 2 |
| #12684 | 59 |