Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1092 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 155 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×#16838152 | C2 | semidirect |
| 2. C2×#16837585 | C2 | semidirect |
| 3. #21426116 | C2 | direct (N × H) |
| 4. C2×#16837200 | C2 | semidirect |
| 5. C2×#16837199 | C2 | semidirect |
| 10. #16838152 | C22 | semidirect |
| 17. #16837585 | C22 | semidirect |
| 20. #16837200 | C22 | semidirect |
| 21. #16837199 | C22 | semidirect |
| 225. C2×C59 | #2203 | semidirect |
| 249. C59 | C2×#2203 | semidirect |
| 439. C2 | #21426116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838152 | 2 |
| C2×#16837585 | 2 |
| #21426116 | 2 |
| C2×#16837200 | 2 |
| C2×#16837199 | 2 |
| C2×C59×#454 | 2 |
| C2×#2203 | 59 |