Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11763889 | C2 | semidirect |
| 2. #11763855 | C2 | semidirect |
| 3. #11763853 | C2 | semidirect |
| 4. D17⋊#108 | C2 | semidirect |
| 5. #11763808 | C2 | semidirect |
| 6. #11763772 | C2 | semidirect |
| 10. #10587680 | C22 | semidirect |
| 15. C2×Q16×C17 | C4 | semidirect |
| 16. C2×#63230 | C4 | semidirect |
| 17. #10587605 | C4 | semidirect |
| 18. #10587605 | C4 | semidirect |
| 21. C2×D136 | C4 | semidirect |
| 23. #10587550 | C22 | semidirect |
| 24. #10587536 | C22 | semidirect |
| 25. #10587535 | C22 | semidirect |
| 26. #10587532 | C22 | semidirect |
| 27. C8×#595 | C22 | semidirect |
| 114. C2×Q16 | #595 | semidirect |
| 129. C17 | #2957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763889 | 2 |
| #11763855 | 2 |
| #11763853 | 2 |
| D17⋊#108 | 2 |
| #11763808 | 2 |
| #11763772 | 2 |
| C2×#10587605 | 2 |
| #2957 | 17 |