Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 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×#15691873 | C2 | semidirect |
| 2. C22×C199⋊C8 | C2 | semidirect |
| 4. #20263886 | C2 | semidirect |
| 5. #20263879 | C2 | semidirect |
| 6. #20263875 | C2 | semidirect |
| 7. C22⋊Q8×C199 | C2 | semidirect |
| 27. C199⋊C8 | D4 | semidirect |
| 39. C22×C199 | SD16 | semidirect |
| 55. C199 | #465 | semidirect |
| 59. C22⋊Q8 | D199 | semidirect |
| 98. C22 | #15691873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691873 | 2 |
| C22×C199⋊C8 | 2 |
| #20263929 | 2 |
| #20263886 | 2 |
| #20263879 | 2 |
| #20263875 | 2 |
| C22⋊Q8×C199 | 2 |
| #465 | 199 |