Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20263920 | C2 | semidirect |
| 3. #20263917 | C2 | semidirect |
| 4. (C22⋊D199)⋊C4 | C2 | semidirect |
| 5. #20263912 | C2 | semidirect |
| 6. C2×C4×Dic199 | C2 | semidirect |
| 7. C42×D199 | C2 | semidirect |
| 8. #117×C199 | C2 | semidirect |
| 9. #15691886 | C4 | semidirect |
| 27. Dic398 | C2×C4 | semidirect |
| 28. D796 | C2×C4 | semidirect |
| 29. C22⋊D199 | C2×C4 | semidirect |
| 35. C4×D199 | C2×C4 | semidirect |
| 37. C2×C4×C199 | C2×C4 | semidirect |
| 51. Dic199 | #41 | semidirect |
| 56. C199 | C4×#41 | semidirect |
| 63. #117 | D199 | semidirect |
| 94. C2×C4 | C4×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| #20263920 | 2 |
| #20263917 | 2 |
| (C22⋊D199)⋊C4 | 2 |
| #20263912 | 2 |
| C2×C4×Dic199 | 2 |
| C42×D199 | 2 |
| #117×C199 | 2 |
| C4×#41 | 199 |