Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1190 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 219 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×#16837602 | C2 | semidirect |
| 3. #21423155 | C2 | direct (N × H) |
| 4. C2×#16837146 | C2 | semidirect |
| 5. C2×Q8⋊(C59⋊C8) | C2 | semidirect |
| 6. C2×C59×#559 | C2 | semidirect |
| 13. #16837602 | C22 | semidirect |
| 17. #16837146 | C22 | semidirect |
| 18. Q8⋊(C59⋊C8) | C22 | semidirect |
| 21. C59×#559 | C22 | semidirect |
| 160. C2×#559 | D59 | semidirect |
| 167. C2×C59 | #1620 | semidirect |
| 175. #559 | C2×D59 | semidirect |
| 191. C59 | C2×#1620 | semidirect |
| 326. C2 | #21423155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837778 | 2 |
| C2×#16837602 | 2 |
| #21423155 | 2 |
| C2×#16837146 | 2 |
| C2×Q8⋊(C59⋊C8) | 2 |
| C2×C59×#559 | 2 |
| C2×#1620 | 59 |