Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. #13092967 | C2 | semidirect |
| 3. #13092804 | C2 | semidirect |
| 4. #13092793 | C2 | semidirect |
| 5. #13092789 | C2 | semidirect |
| 6. C4×#67267 | C2 | semidirect |
| 7. C2×C23×#127 | C2 | semidirect |
| 15. C2×#67273 | C22 | semidirect |
| 17. C2×#67272 | C22 | semidirect |
| 20. #10625046 | C22 | semidirect |
| 21. #10625045 | C22 | semidirect |
| 23. #10625040 | C22 | semidirect |
| 24. #10624985 | C22 | semidirect |
| 25. C4×C23⋊C8 | C22 | semidirect |
| 48. #67267 | D4 | semidirect |
| 71. C23⋊C8 | C2×D4 | semidirect |
| 83. C4×C23 | AGL(1,ℤ/8) | semidirect |
| 88. C2×#127 | D23 | semidirect |
| 116. C23 | #3151 | semidirect |
| 173. C4 | #10625103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625103 | 2 |
| #13092967 | 2 |
| #13092804 | 2 |
| #13092793 | 2 |
| #13092789 | 2 |
| C4×#67267 | 2 |
| C2×C23×#127 | 2 |
| #3151 | 23 |