Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C22×#67273 | C2 | semidirect |
| 2. C23×C23⋊C8 | C2 | semidirect |
| 3. C2×#10625095 | C2 | semidirect |
| 4. #13092644 | C2 | direct (N × H) |
| 5. C2×#10624990 | C2 | semidirect |
| 6. C2×#10624992 | C2 | semidirect |
| 7. C2×#10625014 | C2 | semidirect |
| 19. C2×#67273 | C22 | semidirect |
| 22. #10625095 | C22 | semidirect |
| 27. C22×C23⋊C8 | C22 | semidirect |
| 28. #10625014 | C22 | semidirect |
| 29. #10624992 | C22 | semidirect |
| 30. #10624990 | C22 | semidirect |
| 62. C2×C23⋊C8 | D4 | semidirect |
| 71. C23×C23 | SD16 | semidirect |
| 97. C23⋊C8 | C2×D4 | semidirect |
| 108. C22×C23 | C2×SD16 | semidirect |
| 128. C2×C23 | #465 | semidirect |
| 154. C23 | C2×#465 | semidirect |
| 195. C23 | #67273 | semidirect |
| 230. C22 | C2×#67273 | semidirect |
| 243. C2 | #13092644 | 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 |
| C23×C23⋊C8 | 2 |
| C2×#10625095 | 2 |
| #13092644 | 2 |
| C2×#10624990 | 2 |
| C2×#10624992 | 2 |
| C2×#10625014 | 2 |
| C2×C23×#121 | 2 |
| C2×#465 | 23 |