Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #11763420 | C2 | direct (N × H) |
| 3. C2×#10587556 | C2 | semidirect |
| 4. C2×#10587575 | C2 | semidirect |
| 6. C2×Q8×Dic17 | C2 | semidirect |
| 8. C2×C17×C4⋊Q8 | C2 | semidirect |
| 11. C17×C4⋊Q8 | C22 | semidirect |
| 15. Q8×Dic17 | C22 | semidirect |
| 26. #10587575 | C22 | semidirect |
| 28. #10587556 | C22 | semidirect |
| 83. C2×C4⋊Q8 | D17 | semidirect |
| 90. C2×C17 | #541 | semidirect |
| 96. C4⋊Q8 | C2×D17 | semidirect |
| 114. C17 | C2×#541 | semidirect |
| 168. C2 | #11763420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763420 | 2 |
| C2×#10587584 | 2 |
| C2×#10587556 | 2 |
| C2×#10587575 | 2 |
| C2×#10587632 | 2 |
| C2×Q8×Dic17 | 2 |
| C2×#10587558 | 2 |
| C2×C17×C4⋊Q8 | 2 |
| C2×#541 | 17 |