Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
356 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21425892 | C2 | semidirect |
| 3. #21423984 | C2 | semidirect |
| 4. #21422109 | C2 | semidirect |
| 5. #21422107 | C2 | semidirect |
| 9. #16837803 | C4 | semidirect |
| 10. #16837785 | C4 | semidirect |
| 14. #16837496 | C4 | semidirect |
| 16. D8×Dic59 | C4 | semidirect |
| 188. C59 | #11741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434661 | 2 |
| #21425892 | 2 |
| #21423984 | 2 |
| #21422109 | 2 |
| #21422107 | 2 |
| #21422105 | 2 |
| C59×#1347 | 2 |
| #11741 | 59 |