Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #13092301 | C2 | semidirect |
| 4. #13092285 | C2 | semidirect |
| 5. C4×Dic23⋊C4 | C2 | semidirect |
| 7. C43×C23 | C2 | semidirect |
| 17. #10625047 | C4 | direct (N × H) |
| 32. C42×C23 | C2×C4 | semidirect |
| 36. Dic23⋊C4 | C2×C4 | semidirect |
| 66. C4×C23 | #126 | semidirect |
| 76. C43 | D23 | semidirect |
| 95. C23 | C4×#126 | semidirect |
| 111. C42 | C4×D23 | semidirect |
| 142. C4 | #10625047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625047 | 2 |
| #13092308 | 2 |
| #13092301 | 2 |
| #13092285 | 2 |
| C4×Dic23⋊C4 | 2 |
| C4×(C2×D23)⋊C4 | 2 |
| C43×C23 | 2 |
| C4×#126 | 23 |