Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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. M16×D199 | C2 | semidirect |
| 3. #20263872 | C2 | semidirect |
| 4. #20263871 | C2 | semidirect |
| 5. #100×C199 | C2 | semidirect |
| 12. #15691870 | C22 | semidirect |
| 16. M16×C199 | C22 | semidirect |
| 49. D199 | #100 | direct (N × H) |
| 50. C199 | C2×#100 | semidirect |
| 56. #100 | D199 | direct (N × H) |
| 66. M16 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D199 | 2 |
| M16×D199 | 2 |
| #20263872 | 2 |
| #20263871 | 2 |
| #100×C199 | 2 |
| C2×#100 | 199 |