Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
168 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11763699 | C2 | direct (N × H) |
| 8. C2×#63216 | C4 | semidirect |
| 11. #10587530 | C4 | semidirect |
| 13. C2×C16×C17 | C4 | semidirect |
| 14. C2×#63214 | C4 | semidirect |
| 15. #10587469 | C4 | semidirect |
| 30. #63216 | C2×C4 | semidirect |
| 31. C16×C17 | C2×C4 | semidirect |
| 32. #63214 | C2×C4 | semidirect |
| 61. C2×C17 | #347 | semidirect |
| 74. C2×C16 | #595 | semidirect |
| 77. C17 | C2×#347 | semidirect |
| 93. C16 | C2×#595 | semidirect |
| 119. C2 | #11763699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587530 | 2 |
| C2×#10587532 | 2 |
| #11763699 | 2 |
| C2×#10587469 | 2 |
| C2×#347 | 17 |