Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#67273 | C2 | semidirect |
| 2. C22×#67262 | C2 | semidirect |
| 3. C2×#10625068 | C2 | semidirect |
| 5. #13092662 | C2 | direct (N × H) |
| 6. C2×#10624989 | C2 | semidirect |
| 7. C2×#10624998 | C2 | semidirect |
| 8. C2×C23×#102 | C2 | semidirect |
| 19. C2×#67273 | C22 | semidirect |
| 25. C2×#67262 | C22 | semidirect |
| 27. #10625068 | C22 | semidirect |
| 28. C23×#102 | C22 | semidirect |
| 29. #10624998 | C22 | semidirect |
| 30. #10624989 | C22 | semidirect |
| 62. C2×C23⋊C8 | D4 | semidirect |
| 97. C23⋊C8 | C2×D4 | semidirect |
| 125. C2×#102 | D23 | semidirect |
| 127. C2×C23 | #468 | semidirect |
| 153. #102 | C2×D23 | semidirect |
| 154. C23 | C2×#468 | semidirect |
| 243. C2 | #13092662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67273 | 2 |
| C22×#67262 | 2 |
| C2×#10625068 | 2 |
| C2×#10625109 | 2 |
| #13092662 | 2 |
| C2×#10624989 | 2 |
| C2×#10624998 | 2 |
| C2×C23×#102 | 2 |
| C2×#468 | 23 |