Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20261086 | C2 | semidirect |
| 4. #20261072 | C2 | semidirect |
| 5. #20261030 | C2 | semidirect |
| 6. #20260975 | C2 | semidirect |
| 7. #20260945 | C2 | semidirect |
| 8. #20260889 | C2 | semidirect |
| 10. #103×D97 | C2 | semidirect |
| 11. C4×Q16×C97 | C2 | semidirect |
| 91. D388 | Q16 | semidirect |
| 123. C97 | #3299 | semidirect |
| 132. C4×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261445 | 2 |
| Q8×D388 | 2 |
| #20261086 | 2 |
| #20261072 | 2 |
| #20261030 | 2 |
| #20260975 | 2 |
| #20260945 | 2 |
| #20260889 | 2 |
| C8×D388 | 2 |
| #103×D97 | 2 |
| C4×Q16×C97 | 2 |
| #3299 | 97 |