Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
386 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #21425891 | C2 | semidirect |
| 3. #21425890 | C2 | semidirect |
| 6. #21422209 | C2 | semidirect |
| 7. C59×#1388 | C2 | semidirect |
| 142. #1388 | D59 | semidirect |
| 164. C59 | #12924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837449 | 2 |
| #21425891 | 2 |
| #21425890 | 2 |
| C2×#16837183 | 2 |
| #21424135 | 2 |
| #21422209 | 2 |
| C59×#1388 | 2 |
| #12924 | 59 |