Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 468 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×#16837199 | C2 | semidirect |
| 3. #21422252 | C2 | direct (N × H) |
| 4. C2×C59×#354 | C2 | semidirect |
| 7. C2×#14273724 | C4 | semidirect |
| 10. #16837792 | C4 | semidirect |
| 13. C2×#14273638 | C4 | semidirect |
| 15. #16837199 | C22 | semidirect |
| 19. C59×#354 | C22 | semidirect |
| 34. #14273724 | C2×C4 | semidirect |
| 38. #14273638 | C2×C4 | semidirect |
| 156. C2×#354 | D59 | semidirect |
| 162. C2×C59 | #1406 | semidirect |
| 179. #354 | C2×D59 | semidirect |
| 180. C59 | C2×#1406 | semidirect |
| 319. C2 | #21422252 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837792 | 2 |
| C2×#16837199 | 2 |
| #21422252 | 2 |
| C2×C59×#354 | 2 |
| C2×#1406 | 59 |