Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #20261086 | C2 | semidirect |
| 4. #20261071 | C2 | semidirect |
| 5. #20261031 | C2 | semidirect |
| 6. #20260976 | C2 | semidirect |
| 7. #20260946 | C2 | semidirect |
| 8. #20260893 | C2 | semidirect |
| 9. C4×Dic388 | C2 | semidirect |
| 10. C2×#15690735 | C2 | semidirect |
| 77. D4×C97 | Q16 | semidirect |
| 123. C97 | #3299 | semidirect |
| 208. D4 | Dic388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261442 | 2 |
| D4×Dic194 | 2 |
| #20261086 | 2 |
| #20261071 | 2 |
| #20261031 | 2 |
| #20260976 | 2 |
| #20260946 | 2 |
| #20260893 | 2 |
| C4×Dic388 | 2 |
| C2×#15690735 | 2 |
| C8×D4×C97 | 2 |
| #3299 | 97 |