Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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. Q32×Dic59 | C2 | semidirect |
| 4. #21422295 | C2 | semidirect |
| 6. #21422229 | C2 | semidirect |
| 7. C59×#1416 | C2 | semidirect |
| 11. #16837239 | C4 | semidirect |
| 30. C59⋊C32 | C2×C4 | semidirect |
| 33. Q32×C59 | C2×C4 | semidirect |
| 86. #1416 | D59 | semidirect |
| 105. C59 | #13652 | semidirect |
| 111. Q32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837239 | 2 |
| Q32×Dic59 | 2 |
| #21425942 | 2 |
| #21422295 | 2 |
| #21422275 | 2 |
| #21422229 | 2 |
| C59×#1416 | 2 |
| #13652 | 59 |