Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #21435483 | C2 | semidirect |
| 2. #21434418 | C2 | semidirect |
| 3. #21423324 | C2 | semidirect |
| 4. #21423275 | C2 | semidirect |
| 5. #21422831 | C2 | semidirect |
| 6. #21422547 | C2 | semidirect |
| 8. #16837959 | C22 | semidirect |
| 10. #16837752 | C22 | semidirect |
| 13. #16837682 | C22 | semidirect |
| 15. #16837607 | C22 | semidirect |
| 17. #16837426 | C22 | semidirect |
| 19. C2×C4×C59⋊C8 | C22 | semidirect |
| 20. #16837151 | C22 | semidirect |
| 22. D4⋊(C59⋊C8) | C22 | semidirect |
| 211. C59 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435483 | 2 |
| #21434418 | 2 |
| #21423324 | 2 |
| #21423275 | 2 |
| #21422831 | 2 |
| #21422547 | 2 |
| C59×#3549 | 2 |
| #18691 | 59 |