Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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. #20261087 | C2 | semidirect |
| 4. #20261039 | C2 | semidirect |
| 7. #20260945 | C2 | semidirect |
| 8. Q8×#11715895 | C2 | semidirect |
| 9. C4×#13095501 | C2 | semidirect |
| 11. #557×C97 | C2 | semidirect |
| 116. C97 | #3364 | semidirect |
| 117. #557 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261458 | 2 |
| #20261092 | 2 |
| #20261087 | 2 |
| #20261039 | 2 |
| #20261012 | 2 |
| #20260957 | 2 |
| #20260945 | 2 |
| Q8×#11715895 | 2 |
| C4×#13095501 | 2 |
| C4×#13095498 | 2 |
| #557×C97 | 2 |
| #3364 | 97 |