Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625103 | C2 | semidirect |
| 2. C2×#10625072 | C2 | semidirect |
| 3. #13092684 | C2 | direct (N × H) |
| 4. C2×#10625001 | C2 | semidirect |
| 5. C2×#10625015 | C2 | semidirect |
| 6. C22×D8×C23 | C2 | semidirect |
| 12. C2×D8×C23 | C22 | semidirect |
| 16. #10625103 | C22 | semidirect |
| 21. #10625072 | C22 | semidirect |
| 24. #10625015 | C22 | semidirect |
| 25. #10625001 | C22 | semidirect |
| 104. C22×D8 | D23 | semidirect |
| 112. C2×C23 | #472 | semidirect |
| 124. C2×D8 | C2×D23 | semidirect |
| 134. C23 | C2×#472 | semidirect |
| 215. C2 | #13092684 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625103 | 2 |
| C2×#10625072 | 2 |
| #13092684 | 2 |
| C2×#10625001 | 2 |
| C2×#10625015 | 2 |
| C22×D8×C23 | 2 |
| C2×#472 | 23 |