Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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×#67263 | C2 | semidirect |
| 3. C22×#67273 | C2 | semidirect |
| 4. C2×#10625068 | C2 | semidirect |
| 5. #13092569 | C2 | direct (N × H) |
| 6. C2×#10624991 | C2 | semidirect |
| 7. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 8. C2×C23×#102 | C2 | semidirect |
| 18. C22×Dic46 | C22 | semidirect |
| 19. C22×C8×C23 | C22 | semidirect |
| 20. C2×C4⋊C4×C23 | C22 | semidirect |
| 22. C2×#67273 | C22 | semidirect |
| 25. C22×C23⋊C8 | C22 | semidirect |
| 27. C2×#67263 | C22 | semidirect |
| 29. #10625068 | C22 | semidirect |
| 30. C23×#102 | C22 | semidirect |
| 31. (C2×D23)⋊C8 | C22 | semidirect |
| 32. #10624991 | C22 | semidirect |
| 64. C2×Dic46 | C23 | semidirect |
| 66. C2×C8×C23 | C23 | semidirect |
| 68. C4⋊C4×C23 | C23 | semidirect |
| 73. C2×C23⋊C8 | C23 | semidirect |
| 90. C22×D23 | SD16 | semidirect |
| 134. C2×D23 | C2×SD16 | semidirect |
| 147. C2×#102 | D23 | semidirect |
| 150. C2×C23 | #450 | semidirect |
| 171. C22×C8 | C2×D23 | semidirect |
| 175. C2×C4⋊C4 | C2×D23 | semidirect |
| 178. #102 | C2×D23 | semidirect |
| 180. C23 | C2×#450 | semidirect |
| 218. C2×C8 | C22×D23 | semidirect |
| 221. C4⋊C4 | C22×D23 | semidirect |
| 291. C2 | #13092569 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D23 | 2 |
| C22×#67263 | 2 |
| C22×#67273 | 2 |
| C2×#10625068 | 2 |
| #13092569 | 2 |
| C2×#10624991 | 2 |
| C2×(C2×D23)⋊C8 | 2 |
| C2×C23×#102 | 2 |
| C2×#450 | 23 |