Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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×#15691871 | C2 | semidirect |
| 2. C2×C8×D199 | C2 | semidirect |
| 3. #20263930 | C2 | semidirect |
| 4. #20263926 | C2 | semidirect |
| 5. #20263888 | C2 | semidirect |
| 6. #20263877 | C2 | semidirect |
| 7. #102×C199 | C2 | semidirect |
| 31. C199⋊C8 | D4 | semidirect |
| 47. C2×D199 | D8 | semidirect |
| 59. C199 | #466 | semidirect |
| 67. #102 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691871 | 2 |
| C2×C8×D199 | 2 |
| #20263930 | 2 |
| #20263926 | 2 |
| #20263888 | 2 |
| #20263877 | 2 |
| #102×C199 | 2 |
| #466 | 199 |