Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C22⋊Dic23 | C2 | semidirect |
| 3. #13092296 | C2 | semidirect |
| 4. #13092294 | C2 | semidirect |
| 5. #13092278 | C2 | semidirect |
| 6. #13092272 | C2 | semidirect |
| 7. C22×C22⋊C4×C23 | C2 | semidirect |
| 10. C23×C4×C23 | C22 | semidirect |
| 13. C22×C22⋊D23 | C4 | semidirect |
| 17. C23×Dic23 | C22 | semidirect |
| 20. C2×C22⋊C4×C23 | C22 | semidirect |
| 23. C2×C22⋊Dic23 | C22 | semidirect |
| 24. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 25. C23⋊#95 | C22 | semidirect |
| 36. C23×D23 | C2×C4 | semidirect |
| 46. C2×C22⋊D23 | C2×C4 | semidirect |
| 47. C2×C22⋊D23 | C2×C4 | semidirect |
| 52. C22×Dic23 | C2×C4 | semidirect |
| 66. C23×C23 | C22⋊C4 | semidirect |
| 125. C22×C22⋊C4 | D23 | semidirect |
| 147. C23×C4 | C2×D23 | semidirect |
| 154. C2×C22⋊C4 | C2×D23 | semidirect |
| 156. C23 | #2308 | semidirect |
| 205. C23 | (C2×D23)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D23 | 2 |
| C22×C22⋊Dic23 | 2 |
| #13092296 | 2 |
| #13092294 | 2 |
| #13092278 | 2 |
| #13092272 | 2 |
| C22×C22⋊C4×C23 | 2 |
| #2308 | 23 |