Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. M32×D23 | C2 | semidirect |
| 3. #13092452 | C2 | semidirect |
| 4. #13092228 | C2 | semidirect |
| 5. #13092227 | C2 | semidirect |
| 6. #13092226 | C2 | semidirect |
| 7. C23×#360 | C2 | semidirect |
| 11. #10625090 | C4 | semidirect |
| 12. Q16×D23 | C4 | semidirect |
| 15. #10625083 | C4 | semidirect |
| 16. D8×D23 | C4 | semidirect |
| 20. C23×M32 | C22 | semidirect |
| 21. C23×#106 | C22 | semidirect |
| 22. #10624999 | C22 | semidirect |
| 23. #10624994 | C22 | semidirect |
| 111. #360 | D23 | semidirect |
| 132. M32 | C2×D23 | semidirect |
| 136. #106 | C2×D23 | semidirect |
| 137. C23 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D23 | 2 |
| M32×D23 | 2 |
| #13092452 | 2 |
| #13092228 | 2 |
| #13092227 | 2 |
| #13092226 | 2 |
| C23×#360 | 2 |
| #2145 | 23 |