Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16837226 | C2 | semidirect |
| 5. #21422201 | C2 | semidirect |
| 6. #21422176 | C2 | semidirect |
| 7. C59×#1773 | C2 | semidirect |
| 16. #16837202 | C4 | semidirect |
| 137. #1773 | D59 | semidirect |
| 159. C59 | #13142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837226 | 2 |
| C2×#16837214 | 2 |
| #21425811 | 2 |
| #21424972 | 2 |
| #21422201 | 2 |
| #21422176 | 2 |
| C59×#1773 | 2 |
| #13142 | 59 |