Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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. #13092976 | C2 | semidirect |
| 2. #13092607 | C2 | semidirect |
| 3. #13092604 | C2 | semidirect |
| 4. C2×#10625016 | C2 | semidirect |
| 5. C2×C23×H(5,𝔽2) | C2 | semidirect |
| 11. C22×C22⋊D23 | C22 | semidirect |
| 13. C2×C22⋊Dic23 | C22 | semidirect |
| 15. #10625108 | C22 | semidirect |
| 16. #10625106 | C22 | semidirect |
| 18. #10625016 | C22 | semidirect |
| 20. C24×C23 | D4 | semidirect |
| 22. C23×D23 | C23 | semidirect |
| 31. C2×D4×C23 | D4 | semidirect |
| 34. C22×C4×C23 | D4 | semidirect |
| 39. C22×Dic23 | C23 | semidirect |
| 42. C22⋊Dic23 | C23 | semidirect |
| 88. C2×H(5,𝔽2) | D23 | semidirect |
| 112. C23 | #3026 | semidirect |
| 115. C24 | C22⋊D23 | semidirect |
| 128. C2×D4 | C22⋊D23 | semidirect |
| 133. C22×C4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092976 | 2 |
| #13092607 | 2 |
| #13092604 | 2 |
| C2×#10625016 | 2 |
| C2×C23×H(5,𝔽2) | 2 |
| #3026 | 23 |