Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #11762614 | C2 | semidirect |
| 5. #11762613 | C2 | semidirect |
| 6. #11762612 | C2 | semidirect |
| 7. C17×#358 | C2 | semidirect |
| 12. Q16×D17 | C4 | semidirect |
| 31. Q16×C17 | C2×C4 | semidirect |
| 39. Dic68 | C2×C4 | semidirect |
| 81. #358 | D17 | direct (N × H) |
| 85. D17 | #358 | direct (N × H) |
| 100. C17 | C2×#358 | semidirect |
| 113. Q16 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D17 | 2 |
| C2×C16×D17 | 2 |
| #107×D17 | 2 |
| #11762614 | 2 |
| #11762613 | 2 |
| #11762612 | 2 |
| C17×#358 | 2 |
| C2×#358 | 17 |