Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21437198 | C2 | semidirect |
| 3. #21425812 | C2 | semidirect |
| 4. #21424139 | C2 | semidirect |
| 5. #21422198 | C2 | semidirect |
| 6. #21422197 | C2 | semidirect |
| 7. C59×#2140 | C2 | semidirect |
| 14. #16837652 | C4 | semidirect |
| 43. C2×C59⋊C16 | D4 | semidirect |
| 62. C2×C16×C59 | D4 | semidirect |
| 167. #2140 | D59 | semidirect |
| 195. C59 | #13074 | semidirect |
| 226. C2×C16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437198 | 2 |
| #21433740 | 2 |
| #21425812 | 2 |
| #21424139 | 2 |
| #21422198 | 2 |
| #21422197 | 2 |
| C59×#2140 | 2 |
| #13074 | 59 |