Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21435083 | C2 | semidirect |
| 2. #21434187 | C2 | semidirect |
| 3. #21425014 | C2 | semidirect |
| 4. #21422694 | C2 | semidirect |
| 5. #21422539 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#2540 | C2 | semidirect |
| 38. #14273727 | D4 | semidirect |
| 39. #14273724 | D4 | semidirect |
| 47. C4⋊(C59⋊C8) | D4 | semidirect |
| 57. #14273638 | D4 | semidirect |
| 233. #2540 | D59 | semidirect |
| 271. C59 | #10004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435083 | 2 |
| #21434187 | 2 |
| #21425014 | 2 |
| #21422694 | 2 |
| #21422539 | 2 |
| #21421952 | 2 |
| C59×#2540 | 2 |
| #10004 | 59 |