Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11763722 | C2 | direct (N × H) |
| 7. C2×Q16×C17 | C4 | semidirect |
| 11. Q16×D17 | C4 | semidirect |
| 13. C2×Dic68 | C4 | semidirect |
| 33. Q16×C17 | C2×C4 | semidirect |
| 39. Dic68 | C2×C4 | semidirect |
| 85. C2×C17 | #358 | semidirect |
| 87. D17 | #358 | semidirect |
| 97. C2×Q16 | #595 | semidirect |
| 105. C17 | C2×#358 | semidirect |
| 121. Q16 | C2×#595 | semidirect |
| 169. C2 | #11763722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587529 | 2 |
| C2×#10587534 | 2 |
| #11763722 | 2 |
| C2×Q16×D17 | 2 |
| C2×#358 | 17 |