Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#16837229 | C2 | semidirect |
| 3. C2×#16837208 | C2 | semidirect |
| 4. #21425809 | C2 | semidirect |
| 5. C2×#16837187 | C2 | semidirect |
| 6. #21424157 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 51. C2×C59⋊C16 | D4 | semidirect |
| 183. #1387 | D59 | semidirect |
| 210. C59 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433768 | 2 |
| C2×#16837229 | 2 |
| C2×#16837208 | 2 |
| #21425809 | 2 |
| C2×#16837187 | 2 |
| #21424157 | 2 |
| C59×#1387 | 2 |
| #13385 | 59 |