Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. D4×Dic194 | C2 | semidirect |
| 3. #20261086 | C2 | semidirect |
| 4. #20261066 | C2 | semidirect |
| 5. #20261021 | C2 | semidirect |
| 6. #20260964 | C2 | semidirect |
| 7. #20260941 | C2 | semidirect |
| 8. #20260876 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. C2×#15690735 | C2 | semidirect |
| 11. C8×D4×C97 | C2 | semidirect |
| 79. D4×C97 | SD16 | semidirect |
| 102. Dic194 | #41 | semidirect |
| 129. C97 | #3298 | semidirect |
| 139. C8×D4 | D97 | semidirect |
| 217. D4 | #13095500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic194 | 2 |
| #20261389 | 2 |
| #20261086 | 2 |
| #20261066 | 2 |
| #20261021 | 2 |
| #20260964 | 2 |
| #20260941 | 2 |
| #20260876 | 2 |
| C4×#13095500 | 2 |
| C2×#15690735 | 2 |
| C8×D4×C97 | 2 |
| #3298 | 97 |