Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#67288 | C2 | semidirect |
| 2. C2×#10625103 | C2 | semidirect |
| 3. #13092560 | C2 | semidirect |
| 4. #13092555 | C2 | semidirect |
| 5. #13092550 | C2 | semidirect |
| 6. #13092416 | C2 | semidirect |
| 7. #13092381 | C2 | semidirect |
| 8. C2×C23×#121 | C2 | semidirect |
| 10. C22×D4×C23 | C22 | semidirect |
| 17. C2×#67288 | C22 | semidirect |
| 18. C22×D92 | C22 | semidirect |
| 20. C22×Dic46 | C22 | semidirect |
| 24. C23×#121 | C22 | semidirect |
| 25. C2×C4⋊C4×C23 | C22 | semidirect |
| 27. C2×#67273 | C22 | semidirect |
| 29. C2×#67272 | C22 | semidirect |
| 30. C2×#67267 | C22 | semidirect |
| 31. C22⋊(C23⋊C8) | C22 | semidirect |
| 32. C22⋊(C23⋊C8) | C22 | semidirect |
| 33. #10624992 | C22 | semidirect |
| 34. #10624991 | C22 | semidirect |
| 61. #67288 | D4 | semidirect |
| 115. D92 | C2×D4 | semidirect |
| 120. Dic46 | C2×D4 | semidirect |
| 136. C22×C23 | AGL(1,ℤ/8) | semidirect |
| 150. C2×#121 | D23 | semidirect |
| 173. C22×D4 | C2×D23 | semidirect |
| 183. #121 | C2×D23 | semidirect |
| 184. C2×C4⋊C4 | C2×D23 | semidirect |
| 190. C23 | #3006 | semidirect |
| 294. C22 | #10625103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67288 | 2 |
| C2×#10625103 | 2 |
| #13092560 | 2 |
| #13092555 | 2 |
| #13092550 | 2 |
| #13092416 | 2 |
| #13092381 | 2 |
| C2×C23×#121 | 2 |
| #3006 | 23 |