Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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. C22×#14273719 | C2 | semidirect |
| 2. C2×#16837756 | C2 | direct (N × H) |
| 3. C22×#14273651 | C2 | semidirect |
| 5. C22×C4×C59⋊C8 | C2 | semidirect |
| 9. C2×#14273719 | C22 | semidirect |
| 12. #16837756 | C22 | direct (N × H) |
| 13. C2×#14273651 | C22 | semidirect |
| 15. C2×C4×C59⋊C8 | C22 | semidirect |
| 26. #14273719 | C23 | semidirect |
| 30. #14273651 | C23 | semidirect |
| 32. C4×C59⋊C8 | C23 | semidirect |
| 103. C22×C59 | #488 | semidirect |
| 119. C2×C59 | C2×#488 | semidirect |
| 137. C59 | C22×#488 | semidirect |
| 218. C22 | #16837756 | direct (N × H) |
| 228. C2 | C2×#16837756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273719 | 2 |
| C2×#16837756 | 2 |
| C22×#14273651 | 2 |
| C22×#14273648 | 2 |
| C22×C4×C59⋊C8 | 2 |
| C22×#124×C59 | 2 |
| C22×#488 | 59 |