Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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. C4⋊(C239⋊C8) | C2 | semidirect |
| 5. Dic239⋊C8 | C2 | semidirect |
| 6. Dic239⋊C8 | C2 | semidirect |
| 7. C4⋊C8×C239 | C2 | semidirect |
| 49. C239 | #424 | semidirect |
| 57. C4⋊C8 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838531 | 2 |
| C2×C8×D239 | 2 |
| #21439917 | 2 |
| C4⋊(C239⋊C8) | 2 |
| Dic239⋊C8 | 2 |
| C4⋊C8×C239 | 2 |
| #424 | 239 |