Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11763366 | C2 | semidirect |
| 3. #11763110 | C2 | semidirect |
| 4. #11763100 | C2 | semidirect |
| 5. #11763090 | C2 | semidirect |
| 6. #11762851 | C2 | semidirect |
| 8. C17×#423 | C2 | semidirect |
| 22. #10587556 | C22 | semidirect |
| 23. #10587555 | C22 | semidirect |
| 24. #10587555 | C22 | semidirect |
| 27. C17×C4⋊C8 | C22 | semidirect |
| 28. C17×C4⋊C8 | C22 | semidirect |
| 31. #10587489 | C22 | semidirect |
| 32. #10587488 | C22 | semidirect |
| 40. C2×D68 | Q8 | semidirect |
| 117. #423 | D17 | semidirect |
| 144. C4⋊C8 | C2×D17 | semidirect |
| 145. C4⋊C8 | C2×D17 | semidirect |
| 148. C17 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| C2×C4×D68 | 2 |
| #11763110 | 2 |
| #11763100 | 2 |
| #11763090 | 2 |
| #11762851 | 2 |
| #11762815 | 2 |
| C17×#423 | 2 |
| #3077 | 17 |