Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#15691875 | C2 | semidirect |
| 2. C2×#15691874 | C2 | semidirect |
| 3. C2×#15691871 | C2 | semidirect |
| 4. #20263951 | C2 | semidirect |
| 5. #20263942 | C2 | semidirect |
| 6. #20263865 | C2 | semidirect |
| 7. C2×D8×C199 | C2 | semidirect |
| 29. C199⋊C8 | D4 | semidirect |
| 37. C8×C199 | D4 | semidirect |
| 54. C199 | #496 | semidirect |
| 59. C2×D8 | D199 | semidirect |
| 92. C8 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691875 | 2 |
| C2×#15691874 | 2 |
| C2×#15691871 | 2 |
| #20263951 | 2 |
| #20263942 | 2 |
| #20263865 | 2 |
| C2×D8×C199 | 2 |
| #496 | 199 |