Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13063324 | C2 | semidirect |
| 2. #13063323 | C2 | semidirect |
| 3. #13063315 | C2 | semidirect |
| 7. C4×Dic86 | C2 | semidirect |
| 8. C4×Dic86 | C2 | semidirect |
| 11. C4×Q8×C43 | C2 | semidirect |
| 49. C4×D43 | Q8 | semidirect |
| 71. C43 | #533 | semidirect |
| 80. C4×Q8 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063324 | 2 |
| #13063323 | 2 |
| #13063315 | 2 |
| #13063305 | 2 |
| #13063303 | 2 |
| #13063301 | 2 |
| C4×Dic86 | 2 |
| #13063282 | 2 |
| C42×D43 | 2 |
| C4×Q8×C43 | 2 |
| #533 | 43 |