Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 77 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×#16837199 | C2 | semidirect |
| 2. #21424500 | C2 | semidirect |
| 3. #21424310 | C2 | semidirect |
| 4. #21422223 | C2 | semidirect |
| 33. #14273646 | D4 | semidirect |
| 178. C59 | #13426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837199 | 2 |
| #21424500 | 2 |
| #21424310 | 2 |
| #21422223 | 2 |
| C59×#2733 | 2 |
| #13426 | 59 |