Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
424 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#15690775 | C2 | semidirect |
| 3. #20261048 | C2 | semidirect |
| 4. #20261029 | C2 | semidirect |
| 5. #20260934 | C2 | semidirect |
| 6. #20260876 | C2 | semidirect |
| 7. #20260873 | C2 | semidirect |
| 8. #20260834 | C2 | semidirect |
| 9. #20260832 | C2 | semidirect |
| 10. #20260789 | C2 | semidirect |
| 11. #480×C97 | C2 | semidirect |
| 111. Dic194 | #41 | semidirect |
| 141. C97 | #3112 | semidirect |
| 145. #480 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261280 | 2 |
| C2×#15690775 | 2 |
| #20261048 | 2 |
| #20261029 | 2 |
| #20260934 | 2 |
| #20260876 | 2 |
| #20260873 | 2 |
| #20260834 | 2 |
| #20260832 | 2 |
| #20260789 | 2 |
| #480×C97 | 2 |
| #3112 | 97 |