Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21427069 | C2 | semidirect |
| 3. #21422657 | C2 | semidirect |
| 4. #21422592 | C2 | semidirect |
| 5. #21421998 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1478 | C2 | semidirect |
| 11. #16837607 | C4 | semidirect |
| 12. #16837597 | C4 | semidirect |
| 207. #1478 | D59 | semidirect |
| 238. C59 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433560 | 2 |
| #21427069 | 2 |
| #21422657 | 2 |
| #21422592 | 2 |
| #21421998 | 2 |
| #21421955 | 2 |
| C59×#1478 | 2 |
| #9181 | 59 |