Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10621898 | C2 | semidirect |
| 2. #13063358 | C2 | semidirect |
| 3. #13063353 | C2 | semidirect |
| 4. #13063347 | C2 | semidirect |
| 5. C2×M16×C43 | C2 | semidirect |
| 11. #10621898 | C22 | semidirect |
| 12. C2×D172 | C22 | semidirect |
| 14. C2×Dic86 | C22 | semidirect |
| 15. M16×C43 | C22 | semidirect |
| 16. C2×C8×C43 | C22 | semidirect |
| 17. Dic172 | C22 | semidirect |
| 18. D344 | C22 | semidirect |
| 19. #10621873 | C22 | semidirect |
| 50. C43 | #575 | semidirect |
| 55. C2×M16 | D43 | semidirect |
| 68. M16 | C2×D43 | semidirect |
| 69. C2×C8 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| #13063358 | 2 |
| #13063353 | 2 |
| #13063347 | 2 |
| C2×M16×C43 | 2 |
| #575 | 43 |