Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #11763183 | C2 | semidirect |
| 3. #11763157 | C2 | semidirect |
| 4. #11763009 | C2 | semidirect |
| 5. #11762959 | C2 | semidirect |
| 6. #11762862 | C2 | semidirect |
| 7. C17×#533 | C2 | semidirect |
| 11. C17×C4⋊Q8 | C22 | semidirect |
| 12. C17×C4⋊Q8 | C22 | semidirect |
| 17. C4×Q8×C17 | C22 | semidirect |
| 20. C2×#63230 | C22 | semidirect |
| 26. #10587480 | C22 | semidirect |
| 27. C4⋊#3622 | C22 | semidirect |
| 28. C4×#3622 | C22 | semidirect |
| 69. C2×C4×C17 | SD16 | semidirect |
| 100. #533 | D17 | semidirect |
| 116. C4⋊Q8 | C2×D17 | semidirect |
| 117. C4⋊Q8 | C2×D17 | semidirect |
| 126. C4×Q8 | C2×D17 | semidirect |
| 133. C17 | #3208 | semidirect |
| 180. C2×C4 | #63230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| #11763183 | 2 |
| #11763157 | 2 |
| #11763009 | 2 |
| #11762959 | 2 |
| #11762862 | 2 |
| C17×#533 | 2 |
| #3208 | 17 |