Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 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×#16837834 | C2 | semidirect |
| 2. #21426409 | C2 | direct (N × H) |
| 3. C2×#16837240 | C2 | semidirect |
| 4. C2×#16837237 | C2 | semidirect |
| 5. C2×#16837236 | C2 | semidirect |
| 6. C22×D16×C59 | C2 | semidirect |
| 9. #16837834 | C22 | semidirect |
| 10. C2×Dic472 | C22 | semidirect |
| 12. C2×D944 | C22 | semidirect |
| 13. #16837240 | C22 | semidirect |
| 14. #16837237 | C22 | semidirect |
| 15. #16837236 | C22 | semidirect |
| 16. C2×C59⋊C32 | C22 | semidirect |
| 21. C2×D16×C59 | C22 | semidirect |
| 30. Dic472 | C23 | semidirect |
| 33. D944 | C23 | semidirect |
| 34. C59⋊C32 | C23 | semidirect |
| 111. C22×D16 | D59 | semidirect |
| 118. C2×C59 | #2263 | semidirect |
| 131. C2×D16 | C2×D59 | semidirect |
| 137. C59 | C2×#2263 | semidirect |
| 227. C2 | #21426409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837834 | 2 |
| #21426409 | 2 |
| C2×#16837240 | 2 |
| C2×#16837237 | 2 |
| C2×#16837236 | 2 |
| C22×D16×C59 | 2 |
| C2×#2263 | 59 |