Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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⋊C4×D239 | C2 | semidirect |
| 3. #21439893 | C2 | semidirect |
| 4. #21439882 | C2 | semidirect |
| 5. #21439880 | C2 | semidirect |
| 6. (C2×D239)⋊C8 | C2 | semidirect |
| 7. #107×C239 | C2 | semidirect |
| 52. C239 | #480 | semidirect |
| 57. #107 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439935 | 2 |
| C4⋊C4×D239 | 2 |
| #21439893 | 2 |
| #21439882 | 2 |
| #21439880 | 2 |
| (C2×D239)⋊C8 | 2 |
| #107×C239 | 2 |
| #480 | 239 |