Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22×C4×D199 | C2 | semidirect |
| 3. C2×C22⋊Dic199 | C2 | semidirect |
| 4. C2×(C2×D199)⋊C4 | C2 | semidirect |
| 5. C199⋊#95 | C2 | semidirect |
| 6. C199⋊#95 | C2 | semidirect |
| 7. C2×C22⋊C4×C199 | C2 | semidirect |
| 11. C2×C22⋊D199 | C4 | semidirect |
| 39. C2×Dic199 | C2×C4 | semidirect |
| 40. C2×Dic199 | D4 | semidirect |
| 48. C23×C199 | C2×C4 | semidirect |
| 55. C2×C4×C199 | D4 | semidirect |
| 76. C2×D199 | C22⋊C4 | semidirect |
| 91. C199 | #386 | semidirect |
| 97. C2×C22⋊C4 | D199 | semidirect |
| 129. C23 | C4×D199 | semidirect |
| 147. C2×C4 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D199 | 2 |
| C22×C4×D199 | 2 |
| C2×C22⋊Dic199 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C199⋊#95 | 2 |
| C2×C22⋊C4×C199 | 2 |
| #386 | 199 |