Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
304 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763802 | C2 | semidirect |
| 4. D17⋊#101 | C2 | semidirect |
| 5. #11763691 | C2 | semidirect |
| 6. #11763678 | C2 | semidirect |
| 17. C2×Q16×C17 | C4 | semidirect |
| 18. C2×#63231 | C4 | semidirect |
| 19. C2×#63230 | C4 | semidirect |
| 22. C2×#63219 | C4 | semidirect |
| 131. C2×Q16 | #595 | semidirect |
| 145. C17 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763889 | 2 |
| #11763808 | 2 |
| #11763802 | 2 |
| D17⋊#101 | 2 |
| #11763691 | 2 |
| #11763678 | 2 |
| C2×#10587604 | 2 |
| #1902 | 17 |