Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 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. C22×Dic398 | C2 | semidirect |
| 2. #20263955 | C2 | semidirect |
| 3. #20263954 | C2 | semidirect |
| 4. #20263934 | C2 | semidirect |
| 5. #20263932 | C2 | semidirect |
| 6. C4×Dic398 | C2 | semidirect |
| 28. Dic398 | D4 | direct (N × H) |
| 34. D4×C199 | Q8 | semidirect |
| 42. C22×C199 | C2×Q8 | semidirect |
| 47. C4×C199 | C2×Q8 | semidirect |
| 55. C199 | D4×Q8 | semidirect |
| 86. D4 | Dic398 | direct (N × H) |
| 98. C22 | C2×Dic398 | semidirect |
| 106. C4 | C2×Dic398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic398 | 2 |
| #20263955 | 2 |
| #20263954 | 2 |
| #20263934 | 2 |
| #20263932 | 2 |
| C4×Dic398 | 2 |
| D4×Dic199 | 2 |
| C4×D4×C199 | 2 |
| D4×Q8 | 199 |