Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11763772 | C2 | semidirect |
| 4. #11763691 | C2 | semidirect |
| 9. C22×C8×C17 | C4 | semidirect |
| 10. C2×#63223 | C4 | semidirect |
| 13. C2×#63218 | C4 | semidirect |
| 15. C2×C8×D17 | C4 | semidirect |
| 17. #10587553 | C4 | semidirect |
| 19. #10587545 | C4 | semidirect |
| 108. C22×C8 | #595 | semidirect |
| 116. C17 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763795 | 2 |
| #11763788 | 2 |
| #11763772 | 2 |
| #11763691 | 2 |
| C2×#10587587 | 2 |
| #1757 | 17 |