Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#10625111 | C2 | semidirect |
| 3. C2×D4×Dic23 | C2 | semidirect |
| 4. #13092610 | C2 | direct (N × H) |
| 5. C2×Dic23⋊C8 | C2 | semidirect |
| 6. C2×#10625003 | C2 | semidirect |
| 7. C2×#10625014 | C2 | semidirect |
| 8. C22×D8×C23 | C2 | semidirect |
| 16. C2×D8×C23 | C22 | semidirect |
| 20. #10625111 | C22 | semidirect |
| 22. D4×Dic23 | C22 | semidirect |
| 24. C2×#67272 | C22 | semidirect |
| 28. #10625014 | C22 | semidirect |
| 29. #10625003 | C22 | semidirect |
| 30. Dic23⋊C8 | C22 | semidirect |
| 39. C2×D4×C23 | D4 | semidirect |
| 85. D4×C23 | C2×D4 | semidirect |
| 96. C2×Dic23 | D8 | semidirect |
| 126. Dic23 | C2×D8 | semidirect |
| 128. C22×D8 | D23 | semidirect |
| 137. C2×C23 | #459 | semidirect |
| 151. C2×D8 | C2×D23 | semidirect |
| 164. C23 | C2×#459 | semidirect |
| 181. C2×D4 | C22⋊D23 | semidirect |
| 224. D4 | C2×C22⋊D23 | semidirect |
| 263. C2 | #13092610 | 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 |
| C2×#10625111 | 2 |
| C2×D4×Dic23 | 2 |
| #13092610 | 2 |
| C2×Dic23⋊C8 | 2 |
| C2×#10625003 | 2 |
| C2×#10625014 | 2 |
| C22×D8×C23 | 2 |
| C2×#459 | 23 |