Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 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×#67275 | C2 | semidirect |
| 4. #13092673 | C2 | direct (N × H) |
| 5. C2×#10624990 | C2 | semidirect |
| 6. C2×#10625017 | C2 | semidirect |
| 7. C2×#10624992 | C2 | semidirect |
| 19. C2×#67275 | C22 | semidirect |
| 28. #10625017 | C22 | semidirect |
| 29. #10624992 | C22 | semidirect |
| 30. #10624990 | C22 | semidirect |
| 120. C2×C23 | #470 | semidirect |
| 146. C23 | C2×#470 | semidirect |
| 227. C2 | #13092673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67275 | 2 |
| C22×#67267 | 2 |
| C2×#10625095 | 2 |
| #13092673 | 2 |
| C2×#10624990 | 2 |
| C2×#10625017 | 2 |
| C2×#10624992 | 2 |
| C2×C23×C22⋊Q8 | 2 |
| C2×#470 | 23 |