Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21422661 | C2 | semidirect |
| 4. #21422594 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 12. #16837693 | C4 | semidirect |
| 13. #16837683 | C4 | semidirect |
| 32. #14273727 | C2×C4 | semidirect |
| 33. #14273727 | C2×C4 | semidirect |
| 67. C4⋊C8×C59 | C2×C4 | semidirect |
| 195. #1303 | D59 | semidirect |
| 224. C59 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433895 | 2 |
| #21427007 | 2 |
| #21422661 | 2 |
| #21422594 | 2 |
| #21422488 | 2 |
| #21421956 | 2 |
| C59×#1303 | 2 |
| #9175 | 59 |