Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 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 |
|---|---|---|
| 1. C22×Q8×D23 | C2 | semidirect |
| 2. C22×#67263 | C2 | semidirect |
| 3. C22×#67274 | C2 | semidirect |
| 5. #13092557 | C2 | direct (N × H) |
| 6. C2×#10624992 | C2 | semidirect |
| 7. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 8. C2×C23×#103 | C2 | semidirect |
| 13. C2×Q8×D23 | C22 | semidirect |
| 23. C2×#67274 | C22 | semidirect |
| 27. C2×#67263 | C22 | semidirect |
| 30. C23×#103 | C22 | semidirect |
| 31. (C2×D23)⋊C8 | C22 | semidirect |
| 32. #10624992 | C22 | semidirect |
| 37. C2×Q8×C23 | D4 | semidirect |
| 63. C2×Dic46 | D4 | semidirect |
| 81. C22×D23 | SD16 | semidirect |
| 85. Q8×C23 | C2×D4 | semidirect |
| 109. Dic46 | C2×D4 | semidirect |
| 124. C2×D23 | C2×SD16 | semidirect |
| 138. C2×#103 | D23 | semidirect |
| 140. C2×C23 | #448 | semidirect |
| 168. #103 | C2×D23 | semidirect |
| 170. C23 | C2×#448 | semidirect |
| 184. C2×Q8 | D92 | semidirect |
| 227. Q8 | C2×D92 | semidirect |
| 271. C2 | #13092557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D23 | 2 |
| C22×#67263 | 2 |
| C22×#67274 | 2 |
| C2×#10625066 | 2 |
| #13092557 | 2 |
| C2×#10624992 | 2 |
| C2×(C2×D23)⋊C8 | 2 |
| C2×C23×#103 | 2 |
| C2×#448 | 23 |