Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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×Q16×D23 | C2 | semidirect |
| 3. #13092859 | C2 | direct (N × H) |
| 4. C2×#10625011 | C2 | semidirect |
| 5. C2×#10624982 | C2 | semidirect |
| 6. C2×#10625010 | C2 | semidirect |
| 7. C2×#10624980 | C2 | semidirect |
| 8. C2×C23×Q32 | C2 | semidirect |
| 18. Q16×D23 | C22 | semidirect |
| 22. C23×Q32 | C22 | semidirect |
| 24. #10625011 | C22 | semidirect |
| 25. #10625010 | C22 | semidirect |
| 27. #10624982 | C22 | semidirect |
| 28. #10624980 | C22 | semidirect |
| 98. C2×Q32 | D23 | semidirect |
| 102. C2×C23 | #510 | semidirect |
| 120. Q32 | C2×D23 | semidirect |
| 126. C23 | C2×#510 | semidirect |
| 193. C2 | #13092859 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625090 | 2 |
| C2×Q16×D23 | 2 |
| #13092859 | 2 |
| C2×#10625011 | 2 |
| C2×#10624982 | 2 |
| C2×#10625010 | 2 |
| C2×#10624980 | 2 |
| C2×C23×Q32 | 2 |
| C2×#510 | 23 |