Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#16838537 | C2 | semidirect |
| 2. C2×#16838536 | C2 | semidirect |
| 3. C2×#16838535 | C2 | semidirect |
| 4. #21439958 | C2 | semidirect |
| 6. C8×Dic239 | C2 | semidirect |
| 7. C2×SD16×C239 | C2 | semidirect |
| 29. C239⋊C8 | D4 | semidirect |
| 37. C8×C239 | D4 | semidirect |
| 47. Dic239 | SD16 | semidirect |
| 52. C239 | #492 | semidirect |
| 57. C2×SD16 | D239 | semidirect |
| 90. C8 | C22⋊D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838537 | 2 |
| C2×#16838536 | 2 |
| C2×#16838535 | 2 |
| #21439958 | 2 |
| #21439956 | 2 |
| C8×Dic239 | 2 |
| C2×SD16×C239 | 2 |
| #492 | 239 |