Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 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×D4×D199 | C2 | semidirect |
| 2. C2×#15691871 | C2 | semidirect |
| 3. #20263926 | C2 | semidirect |
| 4. #20263877 | C2 | semidirect |
| 5. #20263876 | C2 | semidirect |
| 6. (C2×D199)⋊C8 | C2 | semidirect |
| 7. C2×D8×C199 | C2 | semidirect |
| 16. C2×C199⋊C8 | C22 | semidirect |
| 17. C4⋊Dic199 | C22 | semidirect |
| 20. C2×D4×C199 | C22 | semidirect |
| 22. C2×C8×C199 | C22 | semidirect |
| 29. D796 | D4 | semidirect |
| 42. D4×C199 | D4 | semidirect |
| 58. C2×D199 | D8 | semidirect |
| 70. C199 | #447 | semidirect |
| 74. C2×D8 | D199 | semidirect |
| 86. C2×D4 | C2×D199 | semidirect |
| 91. C2×C8 | C2×D199 | semidirect |
| 108. D4 | C22⋊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 |
| C2×#15691871 | 2 |
| #20263926 | 2 |
| #20263877 | 2 |
| #20263876 | 2 |
| (C2×D199)⋊C8 | 2 |
| C2×D8×C199 | 2 |
| #447 | 199 |