Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. #21435484 | C2 | semidirect |
| 3. #21434471 | C2 | semidirect |
| 4. #21424935 | C2 | semidirect |
| 5. #21422687 | C2 | semidirect |
| 6. #21422516 | C2 | semidirect |
| 7. C59×#1299 | C2 | semidirect |
| 193. #1299 | D59 | semidirect |
| 223. C59 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435484 | 2 |
| #21435016 | 2 |
| #21434471 | 2 |
| #21424935 | 2 |
| #21422687 | 2 |
| #21422516 | 2 |
| C59×#1299 | 2 |
| #10112 | 59 |