Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 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×#16837800 | C2 | semidirect |
| 3. C2×#16837753 | C2 | semidirect |
| 5. #21423697 | C2 | direct (N × H) |
| 6. C2×C82×C59 | C2 | semidirect |
| 12. #16837800 | C22 | semidirect |
| 16. #16837753 | C22 | semidirect |
| 24. C82×C59 | C22 | semidirect |
| 127. C2×C82 | D59 | semidirect |
| 128. C2×C59 | #1708 | semidirect |
| 149. C82 | C2×D59 | semidirect |
| 150. C59 | C2×#1708 | semidirect |
| 248. C2 | #21423697 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837800 | 2 |
| C2×#16837775 | 2 |
| C2×#16837753 | 2 |
| C2×#16837749 | 2 |
| #21423697 | 2 |
| C2×C82×C59 | 2 |
| C2×#1708 | 59 |