Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C2×#10625097 | C2 | semidirect |
| 3. #13092423 | C2 | direct (N × H) |
| 4. C2×#10625003 | C2 | semidirect |
| 5. C22×M16×C23 | C2 | semidirect |
| 11. C22×D92 | C4 | semidirect |
| 15. C2×M16×C23 | C22 | semidirect |
| 16. C22×C8×C23 | C22 | semidirect |
| 19. #10625097 | C22 | semidirect |
| 20. C2×C4⋊Dic23 | C22 | semidirect |
| 22. #10625003 | C22 | semidirect |
| 42. C2×D92 | C2×C4 | semidirect |
| 46. C2×C8×C23 | C23 | semidirect |
| 49. C4⋊Dic23 | C23 | semidirect |
| 94. C22×M16 | D23 | semidirect |
| 99. C2×C23 | #418 | semidirect |
| 112. C2×M16 | C2×D23 | semidirect |
| 113. C22×C8 | C2×D23 | semidirect |
| 120. C23 | C2×#418 | semidirect |
| 144. C2×C8 | C22×D23 | semidirect |
| 192. C2 | #13092423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D92 | 2 |
| C2×#10625097 | 2 |
| #13092423 | 2 |
| C2×#10625003 | 2 |
| C22×M16×C23 | 2 |
| C2×#418 | 23 |