Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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×#10625015 | C2 | semidirect |
| 3. #13092203 | C2 | direct (N × H) |
| 4. C2×C23×#99 | C2 | semidirect |
| 5. C24×D23 | C4 | semidirect |
| 9. C2×C22⋊Dic23 | C4 | semidirect |
| 12. #10625108 | C4 | semidirect |
| 17. C23×#99 | C22 | semidirect |
| 19. #10625015 | C22 | semidirect |
| 27. C23×D23 | C2×C4 | semidirect |
| 43. C22⋊Dic23 | C2×C4 | semidirect |
| 118. C2×#99 | D23 | semidirect |
| 126. C2×C23 | AΣL(1,𝔽16) | semidirect |
| 143. #99 | C2×D23 | semidirect |
| 144. C23 | C2×AΣL(1,𝔽16) | semidirect |
| 247. C2 | #13092203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625108 | 2 |
| C2×#10625015 | 2 |
| #13092203 | 2 |
| C2×C23×#99 | 2 |
| C2×AΣL(1,𝔽16) | 23 |