Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#10625113 | C2 | semidirect |
| 3. #13092991 | C2 | semidirect |
| 4. #13092578 | C2 | semidirect |
| 5. #13092571 | C2 | semidirect |
| 6. #13092426 | C2 | semidirect |
| 7. #13092414 | C2 | semidirect |
| 8. #13092383 | C2 | semidirect |
| 9. C22×Q16×C23 | C2 | semidirect |
| 138. C22×Q16 | D23 | semidirect |
| 177. C23 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625158 | 2 |
| C2×#10625113 | 2 |
| #13092991 | 2 |
| #13092578 | 2 |
| #13092571 | 2 |
| #13092426 | 2 |
| #13092414 | 2 |
| #13092383 | 2 |
| C22×Q16×C23 | 2 |
| #3011 | 23 |