Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. #20261406 | C2 | semidirect |
| 2. D4×Dic194 | C2 | semidirect |
| 3. #20261082 | C2 | semidirect |
| 4. #20261080 | C2 | semidirect |
| 5. #20261015 | C2 | semidirect |
| 6. #20261014 | C2 | semidirect |
| 7. #20260930 | C2 | semidirect |
| 8. #20260928 | C2 | semidirect |
| 9. C8×Dic194 | C2 | semidirect |
| 10. #20260815 | C2 | semidirect |
| 11. C4×D8×C97 | C2 | semidirect |
| 81. D4×C97 | #41 | semidirect |
| 102. Dic194 | D8 | semidirect |
| 132. C97 | #3358 | semidirect |
| 143. C4×D8 | D97 | semidirect |
| 222. D4 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261406 | 2 |
| D4×Dic194 | 2 |
| #20261082 | 2 |
| #20261080 | 2 |
| #20261015 | 2 |
| #20261014 | 2 |
| #20260930 | 2 |
| #20260928 | 2 |
| C8×Dic194 | 2 |
| #20260815 | 2 |
| C4×D8×C97 | 2 |
| #3358 | 97 |