Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#10587605 | C2 | semidirect |
| 2. C2×#10587497 | C2 | semidirect |
| 3. #11763042 | C2 | semidirect |
| 4. #11762613 | C2 | semidirect |
| 5. #11762611 | C2 | semidirect |
| 6. #11762588 | C2 | semidirect |
| 7. C2×C17×SD32 | C2 | semidirect |
| 33. Q16×C17 | D4 | semidirect |
| 42. D136 | D4 | semidirect |
| 85. C2×SD32 | D17 | semidirect |
| 112. C17 | #2186 | semidirect |
| 123. Q16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587605 | 2 |
| C2×#10587497 | 2 |
| #11763042 | 2 |
| #11762613 | 2 |
| #11762611 | 2 |
| #11762588 | 2 |
| C2×C17×SD32 | 2 |
| #2186 | 17 |