Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. M32×D23 | C2 | semidirect |
| 3. #108×D23 | C2 | semidirect |
| 4. #13092231 | C2 | semidirect |
| 5. #13092230 | C2 | semidirect |
| 6. #13092229 | C2 | semidirect |
| 7. C23×#361 | C2 | semidirect |
| 18. C23×M32 | C22 | semidirect |
| 19. C23×#108 | C22 | semidirect |
| 21. #10625001 | C22 | semidirect |
| 22. #10624994 | C22 | semidirect |
| 97. #361 | D23 | direct (N × H) |
| 103. D23 | #361 | direct (N × H) |
| 116. M32 | C2×D23 | semidirect |
| 120. #108 | C2×D23 | semidirect |
| 121. C23 | C2×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D23 | 2 |
| M32×D23 | 2 |
| #108×D23 | 2 |
| #13092231 | 2 |
| #13092230 | 2 |
| #13092229 | 2 |
| C23×#361 | 2 |
| C2×#361 | 23 |