Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #21433037 | C2 | semidirect |
| 5. #21421954 | C2 | semidirect |
| 6. #21421926 | C2 | semidirect |
| 7. C59×#1518 | C2 | semidirect |
| 9. #16837776 | C4 | semidirect |
| 10. #16837750 | C4 | semidirect |
| 110. C2×C59⋊C8 | SD16 | semidirect |
| 175. #1518 | D59 | semidirect |
| 203. C59 | #9294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435034 | 2 |
| #21433037 | 2 |
| #21424919 | 2 |
| #21422763 | 2 |
| #21421954 | 2 |
| #21421926 | 2 |
| C59×#1518 | 2 |
| #9294 | 59 |