Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#67274 | C2 | semidirect |
| 3. C2×#10625117 | C2 | semidirect |
| 4. #13092566 | C2 | direct (N × H) |
| 5. C2×#10625003 | C2 | semidirect |
| 6. C2×#10625014 | C2 | semidirect |
| 7. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C23 | C2 | semidirect |
| 10. C22×Q8×C23 | C22 | semidirect |
| 20. C2×SD16×C23 | C22 | semidirect |
| 21. C22×C8×C23 | C22 | semidirect |
| 23. #10625117 | C22 | semidirect |
| 25. C2×#67274 | C22 | semidirect |
| 27. C2×C4⋊Dic23 | C22 | semidirect |
| 29. C22×C23⋊C8 | C22 | semidirect |
| 30. #10625014 | C22 | semidirect |
| 31. #10625003 | C22 | semidirect |
| 32. (C2×D23)⋊C8 | C22 | semidirect |
| 43. C2×Q8×C23 | C23 | semidirect |
| 67. C2×C8×C23 | C23 | semidirect |
| 71. C4⋊Dic23 | C23 | semidirect |
| 74. C2×C23⋊C8 | C23 | semidirect |
| 90. C22×D23 | SD16 | semidirect |
| 134. C2×D23 | C2×SD16 | semidirect |
| 143. C22×SD16 | D23 | semidirect |
| 150. C2×C23 | #450 | semidirect |
| 157. C22×Q8 | C2×D23 | semidirect |
| 169. C2×SD16 | C2×D23 | semidirect |
| 171. C22×C8 | C2×D23 | semidirect |
| 180. C23 | C2×#450 | semidirect |
| 191. C2×Q8 | C22×D23 | semidirect |
| 218. C2×C8 | C22×D23 | semidirect |
| 291. C2 | #13092566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D23 | 2 |
| C22×#67274 | 2 |
| C2×#10625117 | 2 |
| #13092566 | 2 |
| C2×#10625003 | 2 |
| C2×#10625014 | 2 |
| C2×(C2×D23)⋊C8 | 2 |
| C22×SD16×C23 | 2 |
| C2×#450 | 23 |