Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763364 | C2 | semidirect |
| 3. #11763171 | C2 | semidirect |
| 4. #11763169 | C2 | semidirect |
| 5. #11763168 | C2 | semidirect |
| 6. #11763165 | C2 | semidirect |
| 7. #11763162 | C2 | semidirect |
| 8. #11762816 | C2 | semidirect |
| 10. #11762761 | C2 | semidirect |
| 11. C17×#489 | C2 | semidirect |
| 14. C17×C4⋊Q8 | C22 | semidirect |
| 23. #10587576 | C22 | semidirect |
| 31. #10587555 | C22 | semidirect |
| 32. C17×#103 | C22 | semidirect |
| 34. C17×#97 | C22 | semidirect |
| 35. #10587506 | C22 | semidirect |
| 38. #10587487 | C22 | semidirect |
| 39. C8×Dic17 | C22 | semidirect |
| 40. #10587481 | C22 | semidirect |
| 42. #10587474 | C22 | semidirect |
| 138. #489 | D17 | semidirect |
| 154. C4⋊Q8 | C2×D17 | semidirect |
| 173. #103 | C2×D17 | semidirect |
| 179. #97 | C2×D17 | semidirect |
| 181. C17 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763364 | 2 |
| #124×D17 | 2 |
| #11763171 | 2 |
| #11763169 | 2 |
| #11763168 | 2 |
| #11763165 | 2 |
| #11763162 | 2 |
| #11762816 | 2 |
| #11762812 | 2 |
| #11762761 | 2 |
| C17×#489 | 2 |
| #3140 | 17 |