Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20261264 | C2 | semidirect |
| 2. #20261137 | C2 | semidirect |
| 3. #20261089 | C2 | semidirect |
| 4. #20260973 | C2 | semidirect |
| 6. #20260961 | C2 | semidirect |
| 7. Q16×Dic97 | C2 | semidirect |
| 8. SD16×Dic97 | C2 | semidirect |
| 9. D8×Dic97 | C2 | semidirect |
| 10. C4×C8×D97 | C2 | semidirect |
| 11. #495×C97 | C2 | semidirect |
| 119. C97 | #3168 | semidirect |
| 122. #495 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261264 | 2 |
| #20261137 | 2 |
| #20261089 | 2 |
| #20260973 | 2 |
| #20260968 | 2 |
| #20260961 | 2 |
| Q16×Dic97 | 2 |
| SD16×Dic97 | 2 |
| D8×Dic97 | 2 |
| C4×C8×D97 | 2 |
| #495×C97 | 2 |
| #3168 | 97 |