Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10625122 | C2 | semidirect |
| 2. C22×#67273 | C2 | semidirect |
| 3. #13092988 | C2 | semidirect |
| 4. #13092579 | C2 | semidirect |
| 5. #13092568 | C2 | semidirect |
| 6. #13092422 | C2 | semidirect |
| 7. #13092413 | C2 | semidirect |
| 8. #13092384 | C2 | semidirect |
| 20. C22×Dic46 | C22 | semidirect |
| 23. C2×#67275 | C22 | semidirect |
| 27. C2×#67273 | C22 | semidirect |
| 28. C2×#67273 | C22 | semidirect |
| 29. #10625097 | C22 | semidirect |
| 30. #10625095 | C22 | semidirect |
| 31. C2×#67267 | C22 | semidirect |
| 32. C22×C23⋊C8 | C22 | semidirect |
| 33. #10625017 | C22 | semidirect |
| 34. #10625014 | C22 | semidirect |
| 35. #10625014 | C22 | semidirect |
| 36. C22⋊(C23⋊C8) | C22 | semidirect |
| 183. C23 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625122 | 2 |
| C22×#67273 | 2 |
| #13092988 | 2 |
| #13092579 | 2 |
| #13092568 | 2 |
| #13092422 | 2 |
| #13092413 | 2 |
| #13092384 | 2 |
| C2×C23×H(5,𝔽2) | 2 |
| #3009 | 23 |