Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 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×#16837775 | C2 | semidirect |
| 3. C2×#16837748 | C2 | semidirect |
| 4. #21423763 | C2 | direct (N × H) |
| 5. C2×#16837123 | C2 | semidirect |
| 6. C2×C59×#493 | C2 | semidirect |
| 12. #16837778 | C22 | semidirect |
| 14. #16837775 | C22 | semidirect |
| 16. #16837748 | C22 | semidirect |
| 19. #16837123 | C22 | semidirect |
| 23. C59×#493 | C22 | semidirect |
| 80. C2×C8×C59 | D8 | semidirect |
| 119. C8×C59 | C2×D8 | semidirect |
| 138. C2×#493 | D59 | semidirect |
| 144. C2×C59 | #1721 | semidirect |
| 157. #493 | C2×D59 | semidirect |
| 166. C59 | C2×#1721 | semidirect |
| 226. C2×C8 | #11745669 | semidirect |
| 262. C8 | C2×#11745669 | semidirect |
| 280. C2 | #21423763 | 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×#16837775 | 2 |
| C2×#16837748 | 2 |
| #21423763 | 2 |
| C2×#16837123 | 2 |
| C2×C59×#493 | 2 |
| C2×#1721 | 59 |