Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#10587550 | C2 | semidirect |
| 3. C2×#10587550 | C2 | semidirect |
| 4. #11763784 | C2 | semidirect |
| 5. #11763685 | C2 | semidirect |
| 6. #11763674 | C2 | semidirect |
| 18. C2×Q16×C17 | C4 | semidirect |
| 19. C2×#63230 | C4 | semidirect |
| 20. C2×#63230 | C4 | semidirect |
| 23. C2×D136 | C4 | semidirect |
| 142. C2×Q16 | #595 | semidirect |
| 159. C17 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587680 | 2 |
| C2×#10587550 | 2 |
| #11763784 | 2 |
| #11763685 | 2 |
| #11763674 | 2 |
| C2×#10587605 | 2 |
| #1876 | 17 |