Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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. C4×D944 | C2 | semidirect |
| 3. #21422297 | C2 | semidirect |
| 4. #21422274 | C2 | semidirect |
| 5. #21422273 | C2 | semidirect |
| 6. #21422230 | C2 | semidirect |
| 7. C4×D16×C59 | C2 | semidirect |
| 10. #16837237 | C4 | semidirect |
| 23. D944 | C2×C4 | semidirect |
| 27. C59⋊C32 | C2×C4 | semidirect |
| 31. D16×C59 | C2×C4 | semidirect |
| 87. C4×D16 | D59 | semidirect |
| 109. C59 | #13654 | semidirect |
| 117. D16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837237 | 2 |
| C4×D944 | 2 |
| #21422297 | 2 |
| #21422274 | 2 |
| #21422273 | 2 |
| #21422230 | 2 |
| C4×D16×C59 | 2 |
| #13654 | 59 |