Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21425022 | C2 | semidirect |
| 3. #21422809 | C2 | semidirect |
| 4. #21422621 | C2 | semidirect |
| 5. #21421966 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#2992 | C2 | semidirect |
| 9. #16837792 | C4 | semidirect |
| 10. #16837768 | C4 | semidirect |
| 210. #2992 | D59 | semidirect |
| 248. C59 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435111 | 2 |
| #21425022 | 2 |
| #21422809 | 2 |
| #21422621 | 2 |
| #21421966 | 2 |
| #21421953 | 2 |
| C59×#2992 | 2 |
| #9378 | 59 |