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. #20261271 | C2 | semidirect |
| 2. #20261136 | C2 | semidirect |
| 3. #20261120 | C2 | semidirect |
| 4. #20261091 | C2 | semidirect |
| 6. #20260966 | C2 | semidirect |
| 7. Q16×Dic97 | C2 | semidirect |
| 8. #20260820 | C2 | semidirect |
| 9. #20260817 | C2 | semidirect |
| 10. C2×C8×Dic97 | C2 | semidirect |
| 11. #467×C97 | C2 | semidirect |
| 119. C97 | #3168 | semidirect |
| 124. #467 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261271 | 2 |
| #20261136 | 2 |
| #20261120 | 2 |
| #20261091 | 2 |
| #20260971 | 2 |
| #20260966 | 2 |
| Q16×Dic97 | 2 |
| #20260820 | 2 |
| #20260817 | 2 |
| C2×C8×Dic97 | 2 |
| #467×C97 | 2 |
| #3168 | 97 |