Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C4⋊Q8×D17 | C2 | semidirect |
| 4. #11763020 | C2 | semidirect |
| 5. #11763018 | C2 | semidirect |
| 6. #11763016 | C2 | semidirect |
| 7. #11763014 | C2 | semidirect |
| 8. #11763012 | C2 | semidirect |
| 9. #11762831 | C2 | semidirect |
| 10. #11762816 | C2 | semidirect |
| 11. C17×#461 | C2 | semidirect |
| 132. C4×C17 | #137 | semidirect |
| 140. Dic17 | #137 | semidirect |
| 149. #461 | D17 | semidirect |
| 189. C17 | #3039 | semidirect |
| 283. C4 | #10587601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587601 | 2 |
| C4⋊Q8×D17 | 2 |
| C4×#63254 | 2 |
| #11763020 | 2 |
| #11763018 | 2 |
| #11763016 | 2 |
| #11763014 | 2 |
| #11763012 | 2 |
| #11762831 | 2 |
| #11762816 | 2 |
| C17×#461 | 2 |
| #3039 | 17 |