Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1838 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 251 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×#16837778 | C2 | semidirect |
| 2. C2×#16837597 | C2 | semidirect |
| 3. #21423150 | C2 | direct (N × H) |
| 4. C2×#16837146 | C2 | semidirect |
| 5. C2×D4⋊(C59⋊C8) | C2 | semidirect |
| 6. C2×D42×C59 | C2 | semidirect |
| 9. C2×#14273724 | C22 | semidirect |
| 11. #16837778 | C22 | semidirect |
| 13. #16837597 | C22 | semidirect |
| 14. C2×C4⋊(C59⋊C8) | C22 | semidirect |
| 16. C2×C4×C59⋊C8 | C22 | semidirect |
| 17. #16837146 | C22 | semidirect |
| 18. D4⋊(C59⋊C8) | C22 | semidirect |
| 22. D42×C59 | C22 | semidirect |
| 37. #14273724 | C23 | semidirect |
| 39. C4⋊(C59⋊C8) | C23 | semidirect |
| 42. C4×C59⋊C8 | C23 | semidirect |
| 87. C2×D4×C59 | D8 | semidirect |
| 140. D4×C59 | C2×D8 | semidirect |
| 181. C2×D42 | D59 | semidirect |
| 189. C2×C59 | #1619 | semidirect |
| 198. D42 | C2×D59 | semidirect |
| 213. C59 | C2×#1619 | semidirect |
| 281. C2×D4 | #11745669 | semidirect |
| 332. D4 | C2×#11745669 | semidirect |
| 370. C2 | #21423150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837778 | 2 |
| C2×#16837597 | 2 |
| #21423150 | 2 |
| C2×#16837146 | 2 |
| C2×D4⋊(C59⋊C8) | 2 |
| C2×D42×C59 | 2 |
| C2×#1619 | 59 |