Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15690831 | C2 | semidirect |
| 2. #20261283 | C2 | semidirect |
| 3. C4×#13095512 | C2 | semidirect |
| 4. #20260955 | C2 | semidirect |
| 5. #20260949 | C2 | semidirect |
| 6. #20260945 | C2 | semidirect |
| 7. #20260941 | C2 | semidirect |
| 8. #20260927 | C2 | semidirect |
| 9. C4⋊C8×D97 | C2 | semidirect |
| 10. #20260728 | C2 | semidirect |
| 11. #460×C97 | C2 | semidirect |
| 45. #13095512 | D4 | semidirect |
| 136. C4×C97 | #135 | semidirect |
| 151. C97 | #3035 | semidirect |
| 159. #460 | D97 | semidirect |
| 292. C4 | #15690831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690831 | 2 |
| #20261283 | 2 |
| C4×#13095512 | 2 |
| #20260955 | 2 |
| #20260949 | 2 |
| #20260945 | 2 |
| #20260941 | 2 |
| #20260927 | 2 |
| C4⋊C8×D97 | 2 |
| #20260728 | 2 |
| #460×C97 | 2 |
| #3035 | 97 |