Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
510 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C2×#16837142 | C2 | semidirect |
| 3. #21422246 | C2 | direct (N × H) |
| 4. C2×C59×#354 | C2 | semidirect |
| 5. C2×#14273775 | C4 | semidirect |
| 9. #16837574 | C4 | semidirect |
| 12. C2×#14273646 | C4 | semidirect |
| 15. #16837142 | C22 | semidirect |
| 19. C59×#354 | C22 | semidirect |
| 23. #14273775 | C2×C4 | semidirect |
| 38. #14273646 | C2×C4 | semidirect |
| 172. C2×#354 | D59 | semidirect |
| 179. C2×C59 | #1404 | semidirect |
| 194. #354 | C2×D59 | semidirect |
| 197. C59 | C2×#1404 | semidirect |
| 353. C2 | #21422246 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837574 | 2 |
| C2×#16837142 | 2 |
| #21422246 | 2 |
| C2×C59×#354 | 2 |
| C2×#1404 | 59 |