Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21439955 | C2 | semidirect |
| 2. #21439951 | C2 | semidirect |
| 3. #21439949 | C2 | semidirect |
| 4. #21439945 | C2 | semidirect |
| 5. #21439936 | C2 | semidirect |
| 7. C4×D956 | C2 | semidirect |
| 8. C4×D956 | C2 | semidirect |
| 9. #21439917 | C2 | semidirect |
| 10. C42×D239 | C2 | semidirect |
| 11. C4×Q8×C239 | C2 | semidirect |
| 74. C239 | #529 | semidirect |
| 82. C4×Q8 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439955 | 2 |
| #21439951 | 2 |
| #21439949 | 2 |
| #21439945 | 2 |
| #21439936 | 2 |
| #21439935 | 2 |
| C4×D956 | 2 |
| #21439917 | 2 |
| C42×D239 | 2 |
| C4×Q8×C239 | 2 |
| #529 | 239 |