Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. Q8×Dic239 | C2 | semidirect |
| 4. #21439893 | C2 | semidirect |
| 6. #21439870 | C2 | semidirect |
| 7. #103×C239 | C2 | semidirect |
| 10. #16838535 | C4 | semidirect |
| 27. C239⋊C8 | C2×C4 | semidirect |
| 29. Q8×C239 | C2×C4 | semidirect |
| 49. C239 | #440 | semidirect |
| 55. #103 | D239 | semidirect |
| 72. Q8 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838535 | 2 |
| Q8×Dic239 | 2 |
| #21439922 | 2 |
| #21439893 | 2 |
| #21439882 | 2 |
| #21439870 | 2 |
| #103×C239 | 2 |
| #440 | 239 |