Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic46 | C2 | semidirect |
| 2. C22×#67263 | C2 | semidirect |
| 4. #13092558 | C2 | direct (N × H) |
| 5. C2×#10624998 | C2 | semidirect |
| 6. C2×C23×C22⋊C8 | C2 | semidirect |
| 15. C22×Dic46 | C22 | semidirect |
| 22. C2×#67263 | C22 | semidirect |
| 23. C23×C22⋊C8 | C22 | semidirect |
| 24. #10624998 | C22 | semidirect |
| 47. C2×Dic46 | D4 | semidirect |
| 57. C23×C23 | SD16 | semidirect |
| 82. Dic46 | C2×D4 | semidirect |
| 90. C22×C23 | C2×SD16 | semidirect |
| 107. C2×C22⋊C8 | D23 | semidirect |
| 109. C2×C23 | #448 | semidirect |
| 131. C22⋊C8 | C2×D23 | semidirect |
| 132. C23 | C2×#448 | semidirect |
| 169. C23 | #67263 | semidirect |
| 201. C22 | C2×#67263 | semidirect |
| 211. C2 | #13092558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic46 | 2 |
| C22×#67263 | 2 |
| C2×#10625101 | 2 |
| #13092558 | 2 |
| C2×#10624998 | 2 |
| C2×C23×C22⋊C8 | 2 |
| C2×#448 | 23 |