Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #21434658 | C2 | semidirect |
| 2. #21434657 | C2 | semidirect |
| 3. #21434605 | C2 | semidirect |
| 5. #21423727 | C2 | semidirect |
| 6. #21423725 | C2 | semidirect |
| 7. #21423724 | C2 | semidirect |
| 8. #21423721 | C2 | semidirect |
| 9. #21423720 | C2 | semidirect |
| 10. #322×D59 | C2 | semidirect |
| 11. C59×#1716 | C2 | semidirect |
| 130. C8×D59 | SD16 | semidirect |
| 181. #1716 | D59 | semidirect |
| 223. C59 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434658 | 2 |
| #21434657 | 2 |
| #21434605 | 2 |
| #21434525 | 2 |
| #21423727 | 2 |
| #21423725 | 2 |
| #21423724 | 2 |
| #21423721 | 2 |
| #21423720 | 2 |
| #322×D59 | 2 |
| C59×#1716 | 2 |
| #19608 | 59 |