Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 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. #11763614 | C2 | semidirect |
| 2. #11763250 | C2 | semidirect |
| 3. #11763244 | C2 | semidirect |
| 4. #11763239 | C2 | semidirect |
| 5. C2×#10587499 | C2 | semidirect |
| 6. #11763226 | C2 | semidirect |
| 7. C17×#578 | C2 | semidirect |
| 11. C17×#135 | C22 | semidirect |
| 12. C2×Q16×C17 | C22 | semidirect |
| 17. #10587500 | C22 | semidirect |
| 18. #10587499 | C22 | semidirect |
| 19. #10587499 | C22 | semidirect |
| 20. #10587498 | C22 | semidirect |
| 21. #10587497 | C22 | semidirect |
| 22. #10587483 | C22 | semidirect |
| 23. C2×#63214 | C22 | semidirect |
| 71. #578 | D17 | semidirect |
| 87. #135 | C2×D17 | semidirect |
| 88. C2×Q16 | C2×D17 | semidirect |
| 98. C17 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763614 | 2 |
| #11763250 | 2 |
| #11763244 | 2 |
| #11763239 | 2 |
| C2×#10587499 | 2 |
| #11763226 | 2 |
| C17×#578 | 2 |
| #3416 | 17 |