Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 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. #21435474 | C2 | semidirect |
| 2. #21434522 | C2 | semidirect |
| 3. #21423241 | C2 | semidirect |
| 4. #21423212 | C2 | semidirect |
| 5. #21423179 | C2 | semidirect |
| 6. #21423150 | C2 | semidirect |
| 7. #21422831 | C2 | semidirect |
| 8. #21422547 | C2 | semidirect |
| 9. C59×#3549 | C2 | semidirect |
| 11. #16837952 | C22 | semidirect |
| 13. #16837781 | C22 | semidirect |
| 15. #16837776 | C22 | semidirect |
| 17. #16837692 | C22 | semidirect |
| 20. #16837597 | C22 | semidirect |
| 22. #16837426 | C22 | semidirect |
| 23. C2×C4×C59⋊C8 | C22 | semidirect |
| 24. #16837151 | C22 | semidirect |
| 26. D4⋊(C59⋊C8) | C22 | semidirect |
| 27. D4⋊(C59⋊C8) | C22 | semidirect |
| 200. #3549 | D59 | semidirect |
| 242. C59 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435474 | 2 |
| #21434522 | 2 |
| #21423241 | 2 |
| #21423212 | 2 |
| #21423179 | 2 |
| #21423150 | 2 |
| #21422831 | 2 |
| #21422547 | 2 |
| C59×#3549 | 2 |
| #18686 | 59 |