Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #21439990 | C2 | semidirect |
| 2. C2×#16838536 | C2 | semidirect |
| 3. #21439967 | C2 | semidirect |
| 4. #21439895 | C2 | semidirect |
| 5. #21439878 | C2 | semidirect |
| 6. #21439877 | C2 | semidirect |
| 51. C239 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439990 | 2 |
| C2×#16838536 | 2 |
| #21439967 | 2 |
| #21439895 | 2 |
| #21439878 | 2 |
| #21439877 | 2 |
| AGL(1,ℤ/8)×C239 | 2 |
| #471 | 239 |