Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#10625119 | C2 | semidirect |
| 2. #13092539 | C2 | semidirect |
| 3. #13092534 | C2 | semidirect |
| 4. #13092466 | C2 | semidirect |
| 5. #13092434 | C2 | semidirect |
| 6. #13092375 | C2 | semidirect |
| 9. C23×#137 | C4 | semidirect |
| 10. C23×AGL(1,ℤ/8) | C4 | semidirect |
| 15. #10625119 | C22 | semidirect |
| 16. #10625119 | C22 | semidirect |
| 22. #10625019 | C22 | semidirect |
| 23. #10625001 | C22 | semidirect |
| 24. #10624997 | C22 | semidirect |
| 25. C8×Dic23 | C22 | semidirect |
| 98. #137 | Dic23 | semidirect |
| 99. AGL(1,ℤ/8) | Dic23 | semidirect |
| 115. C23 | #2955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625119 | 2 |
| #13092539 | 2 |
| #13092534 | 2 |
| #13092466 | 2 |
| #13092434 | 2 |
| #13092375 | 2 |
| C23×#575 | 2 |
| #2955 | 23 |