Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #20260553 | C2 | semidirect |
| 3. #20260553 | C2 | semidirect |
| 5. #20260510 | C2 | semidirect |
| 6. C16×Dic97 | C2 | semidirect |
| 67. C97 | #2164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260690 | 2 |
| #20260553 | 2 |
| C22⋊#13095486 | 2 |
| #20260510 | 2 |
| C16×Dic97 | 2 |
| C22⋊C16×C97 | 2 |
| #2164 | 97 |