Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21422857 | C2 | semidirect |
| 3. #21422697 | C2 | semidirect |
| 4. #21422453 | C2 | semidirect |
| 6. M16×C59⋊C8 | C2 | semidirect |
| 205. C59 | #9789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837756 | 2 |
| #21422857 | 2 |
| #21422697 | 2 |
| #21422453 | 2 |
| #21422448 | 2 |
| M16×C59⋊C8 | 2 |
| C59×#1527 | 2 |
| #9789 | 59 |