Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. #21426897 | C2 | semidirect |
| 4. #21422697 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1288 | C2 | semidirect |
| 10. #16837811 | C4 | semidirect |
| 11. #16837767 | C4 | semidirect |
| 197. #1288 | D59 | semidirect |
| 228. C59 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435288 | 2 |
| #21426897 | 2 |
| #21425015 | 2 |
| #21422697 | 2 |
| #21422642 | 2 |
| #21421951 | 2 |
| C59×#1288 | 2 |
| #9382 | 59 |