Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
568 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20260602 | C2 | semidirect |
| 3. #20260599 | C2 | semidirect |
| 6. C4×#13095490 | C2 | semidirect |
| 8. #20260581 | C2 | semidirect |
| 14. C2×C4×Dic97 | C4 | semidirect |
| 100. C97 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic97 | 2 |
| #20260602 | 2 |
| #20260599 | 2 |
| #20260596 | 2 |
| #20260593 | 2 |
| C4×#13095490 | 2 |
| C4×C22⋊Dic97 | 2 |
| #20260581 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #2283 | 97 |