Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21422861 | C2 | semidirect |
| 5. #21421990 | C2 | semidirect |
| 6. #21421988 | C2 | semidirect |
| 7. C59×#1569 | C2 | semidirect |
| 22. #16837141 | C4 | semidirect |
| 23. #16837141 | C4 | semidirect |
| 24. #16837141 | C4 | semidirect |
| 25. #16837141 | C4 | semidirect |
| 184. #1569 | D59 | semidirect |
| 217. C59 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433166 | 2 |
| #21424927 | 2 |
| #21422861 | 2 |
| #21422687 | 2 |
| #21421990 | 2 |
| #21421988 | 2 |
| C59×#1569 | 2 |
| #8918 | 59 |