Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. C2×#10587499 | C2 | semidirect |
| 3. #11763047 | C2 | semidirect |
| 4. #11762611 | C2 | semidirect |
| 5. #11762610 | C2 | semidirect |
| 6. #11762588 | C2 | semidirect |
| 7. C2×C17×SD32 | C2 | semidirect |
| 9. C2×Q16×C17 | C22 | semidirect |
| 18. C2×C16×C17 | C22 | semidirect |
| 21. #10587489 | C22 | semidirect |
| 22. C2×#63214 | C22 | semidirect |
| 80. C2×D17 | SD32 | semidirect |
| 88. C2×SD32 | D17 | semidirect |
| 100. C2×Q16 | C2×D17 | semidirect |
| 111. C2×C16 | C2×D17 | semidirect |
| 114. C17 | #2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D17 | 2 |
| C2×#10587499 | 2 |
| #11763047 | 2 |
| #11762611 | 2 |
| #11762610 | 2 |
| #11762588 | 2 |
| C2×C17×SD32 | 2 |
| #2187 | 17 |