Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #11762850 | C2 | semidirect |
| 4. #11762848 | C2 | semidirect |
| 5. #11762847 | C2 | semidirect |
| 6. #11762845 | C2 | semidirect |
| 7. C17×#427 | C2 | semidirect |
| 13. C2×#63218 | C4 | semidirect |
| 22. C17×#107 | C22 | semidirect |
| 23. C17×#106 | C22 | semidirect |
| 24. #10587489 | C22 | semidirect |
| 25. #10587488 | C22 | semidirect |
| 26. #10587479 | C22 | semidirect |
| 27. #10587478 | C22 | semidirect |
| 36. C2×C8×C17 | C2×C4 | semidirect |
| 48. C2×#3622 | C2×C4 | semidirect |
| 50. #63218 | C2×C4 | semidirect |
| 51. #63218 | C2×C4 | semidirect |
| 90. #427 | D17 | semidirect |
| 111. #107 | C2×D17 | semidirect |
| 114. #106 | C2×D17 | semidirect |
| 115. C17 | #2911 | semidirect |
| 128. C2×C8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63218 | 2 |
| #117×D17 | 2 |
| #11762850 | 2 |
| #11762848 | 2 |
| #11762847 | 2 |
| #11762845 | 2 |
| C17×#427 | 2 |
| #2911 | 17 |