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×D1888 | C2 | semidirect |
| 3. C2×#16837237 | C2 | semidirect |
| 4. #21426183 | C2 | semidirect |
| 5. #21422273 | C2 | semidirect |
| 6. (C2×D59)⋊C32 | C2 | semidirect |
| 7. C59×#1415 | C2 | semidirect |
| 10. C2×D944 | C22 | semidirect |
| 18. C2×C59⋊C32 | C22 | semidirect |
| 21. C2×C32×C59 | C22 | semidirect |
| 22. C59×#366 | C22 | semidirect |
| 34. D944 | D4 | semidirect |
| 43. D16×C59 | D4 | semidirect |
| 109. C2×D59 | D32 | semidirect |
| 119. #1415 | D59 | semidirect |
| 140. C2×C32 | C2×D59 | semidirect |
| 141. #366 | C2×D59 | semidirect |
| 143. C59 | #13661 | semidirect |
| 159. D16 | D236 | 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×D1888 | 2 |
| C2×#16837237 | 2 |
| #21426183 | 2 |
| #21422273 | 2 |
| (C2×D59)⋊C32 | 2 |
| C59×#1415 | 2 |
| #13661 | 59 |