Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#10625113 | C2 | semidirect |
| 2. C2×#10625103 | C2 | semidirect |
| 3. C2×#10625075 | C2 | semidirect |
| 4. #13092991 | C2 | semidirect |
| 5. #13092984 | C2 | semidirect |
| 6. #13092808 | C2 | semidirect |
| 7. #13092803 | C2 | semidirect |
| 8. #13092798 | C2 | semidirect |
| 9. #13092788 | C2 | semidirect |
| 10. #13092372 | C2 | semidirect |
| 11. C22×SD16×C23 | C2 | semidirect |
| 21. #10625118 | C22 | semidirect |
| 23. #10625115 | C22 | semidirect |
| 24. C2×#67275 | C22 | semidirect |
| 26. C2×#67274 | C22 | semidirect |
| 36. C2×Dic92 | C22 | semidirect |
| 38. C2×D184 | C22 | semidirect |
| 39. C2×#67263 | C22 | semidirect |
| 40. C2×#67263 | C22 | semidirect |
| 41. #10624997 | C22 | semidirect |
| 42. C8×Dic23 | C22 | semidirect |
| 69. C2×C8×C23 | D4 | semidirect |
| 82. #67267 | D4 | semidirect |
| 146. C22×SD16 | D23 | semidirect |
| 191. C23 | #3154 | semidirect |
| 228. C2×C8 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625113 | 2 |
| C2×#10625103 | 2 |
| C2×#10625075 | 2 |
| #13092991 | 2 |
| #13092984 | 2 |
| #13092808 | 2 |
| #13092803 | 2 |
| #13092798 | 2 |
| #13092788 | 2 |
| #13092372 | 2 |
| C22×SD16×C23 | 2 |
| #3154 | 23 |