Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 4. #20263880 | C2 | semidirect |
| 5. #20263879 | C2 | semidirect |
| 6. #20263878 | C2 | semidirect |
| 7. #103×C199 | C2 | semidirect |
| 11. Q8×D199 | C4 | semidirect |
| 25. Dic398 | C2×C4 | semidirect |
| 35. Q8×C199 | C2×C4 | semidirect |
| 54. D199 | #103 | direct (N × H) |
| 55. C199 | C2×#103 | semidirect |
| 63. #103 | D199 | direct (N × H) |
| 83. Q8 | C4×D199 | 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×C8×D199 | 2 |
| C4⋊C4×D199 | 2 |
| #20263880 | 2 |
| #20263879 | 2 |
| #20263878 | 2 |
| #103×C199 | 2 |
| C2×#103 | 199 |