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. #21425813 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. #21424139 | C2 | semidirect |
| 6. #21422197 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 15. #16837656 | C4 | semidirect |
| 49. C2×C59⋊C16 | D4 | semidirect |
| 60. C2×C16×C59 | D4 | semidirect |
| 170. #1384 | D59 | semidirect |
| 195. C59 | #13074 | semidirect |
| 226. C2×C16 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437198 | 2 |
| #21433745 | 2 |
| #21425813 | 2 |
| #21425811 | 2 |
| #21424139 | 2 |
| #21422197 | 2 |
| C59×#1384 | 2 |
| #13074 | 59 |