Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 1. D17⋊#108 | C2 | semidirect |
| 2. C2×#10587534 | C2 | semidirect |
| 4. #11763688 | C2 | semidirect |
| 9. C17×#131 | C4 | semidirect |
| 10. #10587634 | C4 | semidirect |
| 12. #10587593 | C4 | semidirect |
| 16. #10587587 | C4 | semidirect |
| 127. #131 | #595 | semidirect |
| 140. C17 | #1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#108 | 2 |
| C2×#10587534 | 2 |
| #11763800 | 2 |
| #11763688 | 2 |
| #131×D17 | 2 |
| #1816 | 17 |