Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21424929 | C2 | semidirect |
| 3. #21422827 | C2 | semidirect |
| 4. #21422819 | C2 | semidirect |
| 5. #21422609 | C2 | semidirect |
| 6. #21422605 | C2 | semidirect |
| 7. C59×#1536 | C2 | semidirect |
| 9. #16838113 | C4 | semidirect |
| 12. #16838072 | C4 | semidirect |
| 220. #1536 | D59 | semidirect |
| 254. C59 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438494 | 2 |
| #21424929 | 2 |
| #21422827 | 2 |
| #21422819 | 2 |
| #21422609 | 2 |
| #21422605 | 2 |
| C59×#1536 | 2 |
| #8493 | 59 |