Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 326 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. #20260778 | C2 | semidirect |
| 3. C2×#15690738 | C2 | semidirect |
| 4. #20260737 | C2 | semidirect |
| 5. C2×#15690726 | C2 | semidirect |
| 6. #20260637 | C2 | semidirect |
| 7. #339×C97 | C2 | semidirect |
| 46. #13095495 | D4 | semidirect |
| 131. C97 | #2037 | semidirect |
| 138. #339 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261304 | 2 |
| #20260778 | 2 |
| C2×#15690738 | 2 |
| #20260737 | 2 |
| C2×#15690726 | 2 |
| #20260637 | 2 |
| #339×C97 | 2 |
| #2037 | 97 |