Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
394 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21425705 | C2 | semidirect |
| 3. #21424133 | C2 | semidirect |
| 4. #21422114 | C2 | semidirect |
| 5. #21422112 | C2 | semidirect |
| 6. #21422110 | C2 | semidirect |
| 7. C59×#1350 | C2 | semidirect |
| 176. #1350 | D59 | semidirect |
| 205. C59 | #11894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433679 | 2 |
| #21425705 | 2 |
| #21424133 | 2 |
| #21422114 | 2 |
| #21422112 | 2 |
| #21422110 | 2 |
| C59×#1350 | 2 |
| #11894 | 59 |