Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16837781 | C2 | semidirect |
| 3. C2×#16837693 | C2 | semidirect |
| 4. #21423242 | C2 | direct (N × H) |
| 5. C2×#16837129 | C2 | semidirect |
| 6. C2×C59×#333 | C2 | semidirect |
| 17. #16837781 | C22 | semidirect |
| 19. #16837693 | C22 | semidirect |
| 23. #16837129 | C22 | semidirect |
| 26. C59×#333 | C22 | semidirect |
| 156. C2×#333 | D59 | semidirect |
| 158. C2×C59 | #1634 | semidirect |
| 180. #333 | C2×D59 | semidirect |
| 182. C59 | C2×#1634 | semidirect |
| 308. C2 | #21423242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838118 | 2 |
| C2×#16837781 | 2 |
| C2×#16837693 | 2 |
| #21423242 | 2 |
| C2×#16837129 | 2 |
| C2×C59×#333 | 2 |
| C2×#1634 | 59 |