Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
386 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21424271 | C2 | semidirect |
| 3. #21422819 | C2 | semidirect |
| 4. #21422818 | C2 | semidirect |
| 5. #21422706 | C2 | semidirect |
| 6. #21422006 | C2 | semidirect |
| 7. C59×#1530 | C2 | semidirect |
| 162. #1530 | D59 | semidirect |
| 189. C59 | #10524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435474 | 2 |
| #21424271 | 2 |
| #21422819 | 2 |
| #21422818 | 2 |
| #21422706 | 2 |
| #21422006 | 2 |
| C59×#1530 | 2 |
| #10524 | 59 |