Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20261108 | C2 | semidirect |
| 3. #20261030 | C2 | semidirect |
| 4. #20261026 | C2 | semidirect |
| 5. #20260478 | C2 | semidirect |
| 6. #20260464 | C2 | semidirect |
| 7. Q8⋊C8×C97 | C2 | semidirect |
| 53. Q8×C97 | SD16 | semidirect |
| 99. C97 | #1631 | semidirect |
| 105. Q8⋊C8 | D97 | semidirect |
| 153. Q8 | #13095500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261407 | 2 |
| #20261108 | 2 |
| #20261030 | 2 |
| #20261026 | 2 |
| #20260478 | 2 |
| #20260464 | 2 |
| Q8⋊C8×C97 | 2 |
| #1631 | 97 |