Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 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×#67272 | C2 | semidirect |
| 2. C23×C23⋊C8 | C2 | semidirect |
| 3. C2×#10625101 | C2 | semidirect |
| 4. #13092651 | C2 | direct (N × H) |
| 5. C2×#10624989 | C2 | semidirect |
| 6. C2×#10625014 | C2 | semidirect |
| 7. C2×#10624991 | C2 | semidirect |
| 8. C2×C23×#121 | C2 | semidirect |
| 15. C23×#121 | C22 | semidirect |
| 19. C2×#67272 | C22 | semidirect |
| 21. #10625101 | C22 | semidirect |
| 27. C22×C23⋊C8 | C22 | semidirect |
| 28. #10625014 | C22 | semidirect |
| 29. #10624991 | C22 | semidirect |
| 30. #10624989 | C22 | semidirect |
| 63. C2×C23⋊C8 | D4 | semidirect |
| 72. C23×C23 | D8 | semidirect |
| 101. C23⋊C8 | C2×D4 | semidirect |
| 112. C22×C23 | C2×D8 | semidirect |
| 128. C2×#121 | D23 | semidirect |
| 135. C2×C23 | #466 | semidirect |
| 154. #121 | C2×D23 | semidirect |
| 162. C23 | C2×#466 | semidirect |
| 208. C23 | #67272 | semidirect |
| 246. C22 | C2×#67272 | semidirect |
| 259. C2 | #13092651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67272 | 2 |
| C23×C23⋊C8 | 2 |
| C2×#10625101 | 2 |
| #13092651 | 2 |
| C2×#10624989 | 2 |
| C2×#10625014 | 2 |
| C2×#10624991 | 2 |
| C2×C23×#121 | 2 |
| C2×#466 | 23 |