Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
678 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21435011 | C2 | semidirect |
| 2. #21434549 | C2 | semidirect |
| 3. #21425022 | C2 | semidirect |
| 4. #21425016 | C2 | semidirect |
| 5. #21422591 | C2 | semidirect |
| 6. #21421946 | C2 | semidirect |
| 7. C59×#3245 | C2 | semidirect |
| 133. #11745664 | D8 | semidirect |
| 213. #3245 | D59 | semidirect |
| 251. C59 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| #21434549 | 2 |
| #21425022 | 2 |
| #21425016 | 2 |
| #21422591 | 2 |
| #21421946 | 2 |
| C59×#3245 | 2 |
| #10192 | 59 |