Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #21424279 | C2 | semidirect |
| 5. #21421981 | C2 | semidirect |
| 6. #21421942 | C2 | semidirect |
| 7. C59×#1855 | C2 | semidirect |
| 22. #16837140 | C4 | semidirect |
| 23. #16837140 | C4 | semidirect |
| 24. #16837137 | C4 | semidirect |
| 25. #16837137 | C4 | semidirect |
| 212. #1855 | D59 | semidirect |
| 248. C59 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433146 | 2 |
| #21424398 | 2 |
| #21424279 | 2 |
| #21422588 | 2 |
| #21421981 | 2 |
| #21421942 | 2 |
| C59×#1855 | 2 |
| #8875 | 59 |