Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#10587680 | C2 | semidirect |
| 2. #11763853 | C2 | direct (N × H) |
| 3. C2×#10587536 | C2 | semidirect |
| 4. C2×#10587550 | C2 | semidirect |
| 5. C2×C8×#595 | C2 | semidirect |
| 9. #10587680 | C22 | semidirect |
| 15. C2×Q16×C17 | C4 | semidirect |
| 16. C2×#63230 | C4 | semidirect |
| 17. #10587605 | C4 | semidirect |
| 19. C2×D136 | C4 | semidirect |
| 21. #10587550 | C22 | semidirect |
| 22. #10587536 | C22 | semidirect |
| 23. C8×#595 | C22 | semidirect |
| 45. Q16×C17 | C2×C4 | semidirect |
| 47. #63230 | C2×C4 | semidirect |
| 49. D136 | C2×C4 | semidirect |
| 95. C2×C17 | #443 | semidirect |
| 103. C2×Q16 | #595 | semidirect |
| 117. C17 | C2×#443 | semidirect |
| 128. Q16 | C2×#595 | semidirect |
| 185. C2 | #11763853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587680 | 2 |
| #11763853 | 2 |
| C2×#10587536 | 2 |
| C2×#10587550 | 2 |
| C2×C8×#595 | 2 |
| C2×#10587605 | 2 |
| C2×#443 | 17 |