Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #21422628 | C2 | semidirect |
| 4. #21422459 | C2 | semidirect |
| 5. #21422004 | C2 | semidirect |
| 6. #21421973 | C2 | semidirect |
| 10. #16837735 | C4 | semidirect |
| 11. #16837718 | C4 | semidirect |
| 15. #16837557 | C4 | semidirect |
| 16. #16837540 | C4 | semidirect |
| 251. C59 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434922 | 2 |
| #21433158 | 2 |
| #21422628 | 2 |
| #21422459 | 2 |
| #21422004 | 2 |
| #21421973 | 2 |
| C59×#1516 | 2 |
| #9331 | 59 |