Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×D68 | C2 | semidirect |
| 2. #11763125 | C2 | semidirect |
| 3. #11763096 | C2 | semidirect |
| 4. #11763001 | C2 | semidirect |
| 5. #11762942 | C2 | semidirect |
| 6. #11762919 | C2 | semidirect |
| 7. #11762866 | C2 | semidirect |
| 8. C17×#532 | C2 | semidirect |
| 12. C17×C4⋊Q8 | C22 | semidirect |
| 13. C17×#127 | C22 | semidirect |
| 18. C4×D4×C17 | C22 | semidirect |
| 27. #10587503 | C22 | semidirect |
| 30. #10587479 | C22 | semidirect |
| 31. C4⋊#3622 | C22 | semidirect |
| 32. #10587474 | C22 | semidirect |
| 91. D68 | #41 | semidirect |
| 115. #532 | D17 | semidirect |
| 133. C4⋊Q8 | C2×D17 | semidirect |
| 134. #127 | C2×D17 | semidirect |
| 143. C4×D4 | C2×D17 | semidirect |
| 153. C17 | #3109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D68 | 2 |
| #11763125 | 2 |
| #11763096 | 2 |
| #11763001 | 2 |
| #11762942 | 2 |
| #11762919 | 2 |
| #11762866 | 2 |
| C17×#532 | 2 |
| #3109 | 17 |