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×#15690833 | C2 | semidirect |
| 2. #20261286 | C2 | semidirect |
| 3. C4×#13095512 | C2 | semidirect |
| 4. #20260959 | C2 | semidirect |
| 5. #20260953 | C2 | semidirect |
| 6. #20260937 | C2 | semidirect |
| 7. #20260935 | C2 | semidirect |
| 8. #20260931 | C2 | semidirect |
| 9. C4⋊C8×D97 | C2 | semidirect |
| 10. #20260730 | C2 | semidirect |
| 11. #462×C97 | C2 | semidirect |
| 47. #13095512 | D4 | semidirect |
| 137. C4×C97 | #135 | semidirect |
| 151. C97 | #3035 | semidirect |
| 157. #462 | D97 | semidirect |
| 292. C4 | #15690833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| #20261286 | 2 |
| C4×#13095512 | 2 |
| #20260959 | 2 |
| #20260953 | 2 |
| #20260937 | 2 |
| #20260935 | 2 |
| #20260931 | 2 |
| C4⋊C8×D97 | 2 |
| #20260730 | 2 |
| #462×C97 | 2 |
| #3035 | 97 |