Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16837437 | C2 | semidirect |
| 3. C2×#16837212 | C2 | semidirect |
| 4. #21425706 | C2 | semidirect |
| 5. #21422203 | C2 | semidirect |
| 6. #21422202 | C2 | semidirect |
| 7. C2×C59×#360 | C2 | semidirect |
| 12. #16837640 | C4 | semidirect |
| 13. #16837635 | C4 | semidirect |
| 53. #14273659 | D4 | semidirect |
| 70. #106×C59 | D4 | semidirect |
| 187. C2×#360 | D59 | semidirect |
| 216. C59 | #13002 | semidirect |
| 258. #106 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433673 | 2 |
| C2×#16837437 | 2 |
| C2×#16837212 | 2 |
| #21425706 | 2 |
| #21422203 | 2 |
| #21422202 | 2 |
| C2×C59×#360 | 2 |
| #13002 | 59 |