Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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×D184 | C2 | semidirect |
| 2. C22×#67272 | C2 | semidirect |
| 3. C2×#10625111 | C2 | semidirect |
| 4. C2×#10625064 | C2 | semidirect |
| 5. #13092611 | C2 | direct (N × H) |
| 6. C2×Dic23⋊C8 | C2 | semidirect |
| 7. C2×#10624991 | C2 | semidirect |
| 8. C2×C23×#102 | C2 | semidirect |
| 18. #10625111 | C22 | semidirect |
| 20. C2×#67272 | C22 | semidirect |
| 25. C2×D184 | C22 | semidirect |
| 27. #10625064 | C22 | semidirect |
| 28. C23×#102 | C22 | semidirect |
| 29. Dic23⋊C8 | C22 | semidirect |
| 30. #10624991 | C22 | semidirect |
| 51. C2×D92 | D4 | semidirect |
| 92. C2×Dic23 | D8 | semidirect |
| 100. D92 | C2×D4 | semidirect |
| 126. Dic23 | C2×D8 | semidirect |
| 134. C2×#102 | D23 | semidirect |
| 136. C2×C23 | #459 | semidirect |
| 163. #102 | C2×D23 | semidirect |
| 164. C23 | C2×#459 | semidirect |
| 263. C2 | #13092611 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D184 | 2 |
| C22×#67272 | 2 |
| C2×#10625111 | 2 |
| C2×#10625064 | 2 |
| #13092611 | 2 |
| C2×Dic23⋊C8 | 2 |
| C2×#10624991 | 2 |
| C2×C23×#102 | 2 |
| C2×#459 | 23 |