Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×D136 | C2 | semidirect |
| 2. #11763373 | C2 | semidirect |
| 3. #11763062 | C2 | semidirect |
| 4. #11763045 | C2 | semidirect |
| 5. #11762847 | C2 | semidirect |
| 6. #11762815 | C2 | semidirect |
| 7. C2×C17×#131 | C2 | semidirect |
| 12. C2×M16×C17 | C22 | semidirect |
| 14. C22×C8×C17 | C22 | semidirect |
| 18. #10587616 | C22 | semidirect |
| 23. #10587492 | C22 | semidirect |
| 24. #10587489 | C22 | semidirect |
| 25. #10587488 | C22 | semidirect |
| 42. C2×C8×C17 | D4 | semidirect |
| 90. C2×#131 | D17 | semidirect |
| 108. C2×M16 | C2×D17 | semidirect |
| 110. C22×C8 | C2×D17 | semidirect |
| 119. C17 | #3058 | semidirect |
| 138. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D136 | 2 |
| #11763373 | 2 |
| #11763062 | 2 |
| #11763045 | 2 |
| #11762847 | 2 |
| #11762815 | 2 |
| C2×C17×#131 | 2 |
| #3058 | 17 |