Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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. #13092539 | C2 | semidirect |
| 2. #13092529 | C2 | semidirect |
| 3. #13092240 | C2 | semidirect |
| 4. #13092230 | C2 | semidirect |
| 5. #13092227 | C2 | semidirect |
| 6. #13092194 | C2 | semidirect |
| 12. C23×SD32 | C4 | semidirect |
| 13. C23×D16 | C4 | semidirect |
| 24. Q16×C23 | C2×C4 | semidirect |
| 28. D8×C23 | C2×C4 | semidirect |
| 37. C16×C23 | C2×C4 | semidirect |
| 80. SD32 | Dic23 | semidirect |
| 81. D16 | Dic23 | semidirect |
| 89. C23 | AGL(1,ℤ/16) | semidirect |
| 93. Q16 | C2×Dic23 | semidirect |
| 97. D8 | C2×Dic23 | semidirect |
| 107. C16 | C2×Dic23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092539 | 2 |
| #13092529 | 2 |
| #13092240 | 2 |
| #13092230 | 2 |
| #13092227 | 2 |
| #13092194 | 2 |
| C23×#509 | 2 |
| AGL(1,ℤ/16) | 23 |