Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21426416 | C2 | semidirect |
| 3. C2×#16837241 | C2 | semidirect |
| 4. #21426221 | C2 | semidirect |
| 5. #21422287 | C2 | semidirect |
| 6. #21422281 | C2 | semidirect |
| 7. C59×#1401 | C2 | semidirect |
| 13. C2×Dic472 | C22 | semidirect |
| 20. #16837232 | C22 | semidirect |
| 23. C59×M64 | C22 | semidirect |
| 24. C2×C32×C59 | C22 | semidirect |
| 121. #1401 | D59 | semidirect |
| 140. M64 | C2×D59 | semidirect |
| 141. C2×C32 | C2×D59 | semidirect |
| 144. C59 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437237 | 2 |
| #21426416 | 2 |
| C2×#16837241 | 2 |
| #21426221 | 2 |
| #21422287 | 2 |
| #21422281 | 2 |
| C59×#1401 | 2 |
| #13671 | 59 |