Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D17 | C2 | semidirect |
| 4. #11763068 | C2 | semidirect |
| 5. #11763067 | C2 | semidirect |
| 6. #11763064 | C2 | semidirect |
| 7. #11763049 | C2 | semidirect |
| 8. #11763048 | C2 | semidirect |
| 9. #11762844 | C2 | semidirect |
| 10. #11762816 | C2 | semidirect |
| 11. C17×#470 | C2 | semidirect |
| 135. #470 | D17 | semidirect |
| 174. C17 | #3059 | 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×#10587593 | 2 |
| #11763382 | 2 |
| #11763068 | 2 |
| #11763067 | 2 |
| #11763064 | 2 |
| #11763049 | 2 |
| #11763048 | 2 |
| #11762844 | 2 |
| #11762816 | 2 |
| C17×#470 | 2 |
| #3059 | 17 |