Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
334 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×D16×D59 | C2 | semidirect |
| 2. C2×#16837237 | C2 | semidirect |
| 3. #21426179 | C2 | semidirect |
| 4. #21422275 | C2 | semidirect |
| 5. #21422274 | C2 | semidirect |
| 6. (C2×D59)⋊C32 | C2 | semidirect |
| 7. C2×C59×D32 | C2 | semidirect |
| 16. C2×C59⋊C32 | C22 | semidirect |
| 17. #16837228 | C22 | semidirect |
| 20. C2×D16×C59 | C22 | semidirect |
| 22. C2×C32×C59 | C22 | semidirect |
| 31. D944 | D4 | semidirect |
| 44. D16×C59 | D4 | semidirect |
| 109. C2×D59 | D32 | semidirect |
| 116. C2×D32 | D59 | semidirect |
| 134. C2×D16 | C2×D59 | semidirect |
| 140. C2×C32 | C2×D59 | semidirect |
| 143. C59 | #13661 | semidirect |
| 159. D16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D59 | 2 |
| C2×#16837237 | 2 |
| #21426179 | 2 |
| #21422275 | 2 |
| #21422274 | 2 |
| (C2×D59)⋊C32 | 2 |
| C2×C59×D32 | 2 |
| #13661 | 59 |