Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #13092308 | C2 | semidirect |
| 3. #13092306 | C2 | semidirect |
| 4. #13092275 | C2 | semidirect |
| 6. C4×C22⋊Dic23 | C2 | semidirect |
| 7. C4×C22⋊C4×C23 | C2 | semidirect |
| 12. C2×C42×C23 | C22 | semidirect |
| 14. C2×(C2×D23)⋊C4 | C4 | semidirect |
| 19. C2×Dic23⋊C4 | C22 | semidirect |
| 20. C2×C4×Dic23 | C22 | semidirect |
| 21. C23×#95 | C22 | semidirect |
| 22. C23⋊#95 | C22 | semidirect |
| 23. C23⋊#95 | C22 | semidirect |
| 100. C4×C22⋊C4 | D23 | semidirect |
| 119. C2×C42 | C2×D23 | semidirect |
| 122. #95 | C2×D23 | semidirect |
| 123. C23 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D23)⋊C4 | 2 |
| #13092308 | 2 |
| #13092306 | 2 |
| #13092275 | 2 |
| #13092272 | 2 |
| C4×C22⋊Dic23 | 2 |
| C4×C22⋊C4×C23 | 2 |
| #2312 | 23 |