Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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×#67274 | C2 | semidirect |
| 3. #13092791 | C2 | direct (N × H) |
| 4. C2×C4×C23⋊C8 | C2 | semidirect |
| 5. C2×C23×C4⋊Q8 | C2 | semidirect |
| 10. C23×C4⋊Q8 | C22 | semidirect |
| 14. C2×#67274 | C22 | semidirect |
| 18. C4×C23⋊C8 | C22 | semidirect |
| 35. C2×C23⋊C8 | D4 | semidirect |
| 45. C2×C4×C23 | SD16 | semidirect |
| 53. C23⋊C8 | C2×D4 | semidirect |
| 63. C4×C23 | C2×SD16 | semidirect |
| 66. C2×C4⋊Q8 | D23 | semidirect |
| 70. C2×C23 | #492 | semidirect |
| 81. C4⋊Q8 | C2×D23 | semidirect |
| 87. C23 | C2×#492 | semidirect |
| 117. C2×C4 | #67274 | semidirect |
| 131. C4 | C2×#67274 | semidirect |
| 134. C2 | #13092791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67274 | 2 |
| C2×#10625045 | 2 |
| #13092791 | 2 |
| C2×C4×C23⋊C8 | 2 |
| C2×C23×C4⋊Q8 | 2 |
| C2×#492 | 23 |