Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#10587634 | C2 | semidirect |
| 2. #11763292 | C2 | semidirect |
| 3. #11762814 | C2 | semidirect |
| 4. #11762810 | C2 | semidirect |
| 5. #11762805 | C2 | semidirect |
| 6. C2×#10587503 | C2 | semidirect |
| 9. C17×H(5,𝔽2) | C4 | semidirect |
| 18. #10587612 | C22 | semidirect |
| 19. C2×C4⋊Dic17 | C22 | semidirect |
| 20. C2×#63223 | C22 | semidirect |
| 21. C22×#3622 | C22 | semidirect |
| 22. #10587506 | C22 | semidirect |
| 23. #10587506 | C22 | semidirect |
| 24. #10587503 | C22 | semidirect |
| 25. #10587503 | C22 | semidirect |
| 26. #10587503 | C22 | semidirect |
| 31. #41×C17 | C2×C4 | semidirect |
| 39. C2×D4×C17 | C2×C4 | semidirect |
| 106. H(5,𝔽2) | Dic17 | semidirect |
| 124. C17 | #2897 | semidirect |
| 129. #41 | C2×Dic17 | semidirect |
| 137. C2×D4 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587634 | 2 |
| #11763292 | 2 |
| #11762814 | 2 |
| #11762810 | 2 |
| #11762805 | 2 |
| C2×#10587503 | 2 |
| C2×C17×H(5,𝔽2) | 2 |
| #2897 | 17 |