Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21435095 | C2 | semidirect |
| 3. #21423411 | C2 | semidirect |
| 4. #21422723 | C2 | semidirect |
| 5. #21422693 | C2 | semidirect |
| 6. C59×#3166 | C2 | semidirect |
| 14. #16837794 | C22 | semidirect |
| 15. #16837764 | C22 | semidirect |
| 20. #16837144 | C22 | semidirect |
| 21. #16837141 | C22 | semidirect |
| 24. C59×#501 | C22 | semidirect |
| 150. #3166 | D59 | semidirect |
| 167. #501 | C2×D59 | semidirect |
| 179. C59 | #19006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838150 | 2 |
| #21435095 | 2 |
| #21423411 | 2 |
| #21422723 | 2 |
| #21422693 | 2 |
| C59×#3166 | 2 |
| #19006 | 59 |