Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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. C22×#67275 | C2 | semidirect |
| 3. #13092796 | C2 | semidirect |
| 4. #13092656 | C2 | semidirect |
| 5. #13092627 | C2 | semidirect |
| 6. #13092624 | C2 | semidirect |
| 7. #13092573 | C2 | semidirect |
| 8. #13092572 | C2 | semidirect |
| 9. C4×#67275 | C2 | semidirect |
| 71. #67275 | D4 | direct (N × H) |
| 88. D4×C23 | Q16 | semidirect |
| 114. C22×C23 | C2×Q16 | semidirect |
| 121. C4×C23 | C2×Q16 | semidirect |
| 172. C23 | D4×Q16 | semidirect |
| 224. D4 | #67275 | direct (N × H) |
| 244. C22 | C2×#67275 | semidirect |
| 254. C4 | C2×#67275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67275 | 2 |
| D4×Dic46 | 2 |
| #13092796 | 2 |
| #13092656 | 2 |
| #13092627 | 2 |
| #13092624 | 2 |
| #13092573 | 2 |
| #13092572 | 2 |
| C4×#67275 | 2 |
| D4×C23⋊C8 | 2 |
| D4×Q8×C23 | 2 |
| D4×Q16 | 23 |