Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21434841 | C2 | semidirect |
| 3. #21426316 | C2 | semidirect |
| 4. #21426268 | C2 | semidirect |
| 5. #21426178 | C2 | semidirect |
| 7. #21425989 | C2 | semidirect |
| 8. C59×#2165 | C2 | semidirect |
| 13. #16837800 | C22 | semidirect |
| 14. #16837782 | C22 | semidirect |
| 23. #16837510 | C22 | semidirect |
| 26. #16837225 | C22 | semidirect |
| 27. #16837219 | C22 | semidirect |
| 30. C59×#364 | C22 | semidirect |
| 32. C59×#347 | C22 | semidirect |
| 165. #2165 | D59 | semidirect |
| 189. #364 | C2×D59 | semidirect |
| 193. #347 | C2×D59 | semidirect |
| 194. C59 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434841 | 2 |
| #21433007 | 2 |
| #21426316 | 2 |
| #21426268 | 2 |
| #21426178 | 2 |
| #21426049 | 2 |
| #21425989 | 2 |
| C59×#2165 | 2 |
| #33689 | 59 |