Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21432664 | C2 | direct (N × H) |
| 3. C2×#16837429 | C2 | semidirect |
| 4. C2×#16837426 | C2 | semidirect |
| 5. C22×C4⋊(C59⋊C8) | C2 | semidirect |
| 11. #16837429 | C22 | semidirect |
| 12. #16837426 | C22 | semidirect |
| 17. C2×C4⋊(C59⋊C8) | C22 | semidirect |
| 113. C2×C4×C59 | #131 | semidirect |
| 141. C4×C59 | C2×#131 | semidirect |
| 151. C2×C59 | #2906 | semidirect |
| 175. C59 | C2×#2906 | semidirect |
| 262. C2×C4 | #14273734 | semidirect |
| 289. C4 | C2×#14273734 | semidirect |
| 293. C2 | #21432664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273734 | 2 |
| #21432664 | 2 |
| C2×#16837429 | 2 |
| C2×#16837426 | 2 |
| C22×C4⋊(C59⋊C8) | 2 |
| C2×C4×#41×C59 | 2 |
| C2×#2906 | 59 |