Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21422083 | C2 | semidirect |
| 4. #21422080 | C2 | semidirect |
| 5. C2×C59×H(3,ℤ/4) | C2 | semidirect |
| 6. C2×#14273749 | C4 | semidirect |
| 9. #16837660 | C4 | semidirect |
| 11. #16837655 | C4 | semidirect |
| 15. #16837440 | C4 | semidirect |
| 26. C2×Dic236 | C2×C4 | semidirect |
| 28. C2×D472 | C2×C4 | semidirect |
| 42. #14273659 | C2×C4 | semidirect |
| 43. #14273659 | C2×C4 | semidirect |
| 188. C2×H(3,ℤ/4) | D59 | semidirect |
| 215. C59 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433705 | 2 |
| C2×#16837184 | 2 |
| #21422083 | 2 |
| #21422080 | 2 |
| C2×C59×H(3,ℤ/4) | 2 |
| #11685 | 59 |