Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16837184 | C2 | semidirect |
| 3. #21422080 | C2 | direct (N × H) |
| 4. C2×C59×H(3,ℤ/4) | C2 | semidirect |
| 5. C22×D472 | C4 | semidirect |
| 10. #16837655 | C4 | semidirect |
| 12. C2×#14273659 | C4 | semidirect |
| 15. #16837184 | C22 | semidirect |
| 19. C59×H(3,ℤ/4) | C22 | semidirect |
| 25. C2×D472 | C2×C4 | semidirect |
| 36. #14273659 | C2×C4 | semidirect |
| 172. C2×H(3,ℤ/4) | D59 | semidirect |
| 178. C2×C59 | #1339 | semidirect |
| 195. H(3,ℤ/4) | C2×D59 | semidirect |
| 196. C59 | C2×#1339 | semidirect |
| 351. C2 | #21422080 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837655 | 2 |
| C2×#16837184 | 2 |
| #21422080 | 2 |
| C2×C59×H(3,ℤ/4) | 2 |
| C2×#1339 | 59 |