Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 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×#67262 | C2 | semidirect |
| 2. C2×#10625109 | C2 | semidirect |
| 3. #13092667 | C2 | direct (N × H) |
| 4. C2×#10624999 | C2 | semidirect |
| 5. C2×#10625014 | C2 | semidirect |
| 6. C22×D8×C23 | C2 | semidirect |
| 11. C2×D8×C23 | C22 | semidirect |
| 15. #10625109 | C22 | semidirect |
| 19. C2×#67262 | C22 | semidirect |
| 20. #10625014 | C22 | semidirect |
| 21. #10624999 | C22 | semidirect |
| 38. C2×C8×C23 | D4 | semidirect |
| 69. C8×C23 | C2×D4 | semidirect |
| 87. C22×D8 | D23 | semidirect |
| 94. C2×C23 | #469 | semidirect |
| 102. C2×D8 | C2×D23 | semidirect |
| 113. C23 | C2×#469 | semidirect |
| 133. C2×C8 | C22⋊D23 | semidirect |
| 162. C8 | C2×C22⋊D23 | semidirect |
| 180. C2 | #13092667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67262 | 2 |
| C2×#10625109 | 2 |
| #13092667 | 2 |
| C2×#10624999 | 2 |
| C2×#10625014 | 2 |
| C22×D8×C23 | 2 |
| C2×#469 | 23 |