Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 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. #21425707 | C2 | semidirect |
| 3. #21422104 | C2 | semidirect |
| 4. C59×#1807 | C2 | semidirect |
| 5. C22×D472 | C4 | semidirect |
| 10. #16837638 | C4 | semidirect |
| 12. C2×#14273661 | C4 | semidirect |
| 15. C22⋊(C59⋊C16) | C22 | semidirect |
| 19. C59×#340 | C22 | semidirect |
| 150. #1807 | D59 | semidirect |
| 173. #340 | C2×D59 | semidirect |
| 174. C59 | #11888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837638 | 2 |
| #21425707 | 2 |
| #21422104 | 2 |
| C59×#1807 | 2 |
| #11888 | 59 |