Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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. C4×D1732 | C2 | semidirect |
| 3. #28357153 | C2 | semidirect |
| 4. #28357141 | C2 | semidirect |
| 5. #28357140 | C2 | semidirect |
| 6. C4×#16812358 | C2 | semidirect |
| 7. C4×D4×C433 | C2 | semidirect |
| 10. #20294082 | C4 | direct (N × H) |
| 22. D1732 | C2×C4 | semidirect |
| 26. #16812358 | C2×C4 | semidirect |
| 29. D4×C433 | C2×C4 | semidirect |
| 44. C4×C433 | D8 | semidirect |
| 53. C433 | C4×D8 | semidirect |
| 57. C4×D4 | D433 | semidirect |
| 79. D4 | C4×D433 | semidirect |
| 99. C4 | #20294082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294082 | 2 |
| C4×D1732 | 2 |
| #28357153 | 2 |
| #28357141 | 2 |
| #28357140 | 2 |
| C4×#16812358 | 2 |
| C4×D4×C433 | 2 |
| C4×D8 | 433 |