Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×Q8×D199 | C2 | semidirect |
| 2. C2×#15691875 | C2 | semidirect |
| 3. C2×#15691873 | C2 | semidirect |
| 5. #20263878 | C2 | semidirect |
| 6. (C2×D199)⋊C8 | C2 | semidirect |
| 7. #103×C199 | C2 | semidirect |
| 27. Dic398 | D4 | semidirect |
| 38. Q8×C199 | D4 | semidirect |
| 49. C2×D199 | SD16 | semidirect |
| 61. C199 | #448 | semidirect |
| 68. #103 | D199 | semidirect |
| 91. Q8 | D796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D199 | 2 |
| C2×#15691875 | 2 |
| C2×#15691873 | 2 |
| #20263930 | 2 |
| #20263878 | 2 |
| (C2×D199)⋊C8 | 2 |
| #103×C199 | 2 |
| #448 | 199 |