Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #21422660 | C2 | semidirect |
| 5. #21421956 | C2 | semidirect |
| 6. #21421925 | C2 | semidirect |
| 7. C59×#1995 | C2 | semidirect |
| 10. #16837776 | C4 | semidirect |
| 11. #16837750 | C4 | semidirect |
| 48. C4×C59⋊C8 | C2×C4 | semidirect |
| 52. C4⋊Q8×C59 | C2×C4 | semidirect |
| 53. C4⋊Q8×C59 | C2×C4 | semidirect |
| 105. C42×C59 | SD16 | semidirect |
| 191. #1995 | D59 | semidirect |
| 221. C59 | #9295 | semidirect |
| 228. C4⋊Q8 | C4×D59 | semidirect |
| 229. C4⋊Q8 | C4×D59 | semidirect |
| 308. C42 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435034 | 2 |
| #21426821 | 2 |
| #21422765 | 2 |
| #21422660 | 2 |
| #21421956 | 2 |
| #21421925 | 2 |
| C59×#1995 | 2 |
| #9295 | 59 |