Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11763470 | C2 | semidirect |
| 3. #11763194 | C2 | semidirect |
| 4. #11763047 | C2 | semidirect |
| 5. #11763045 | C2 | semidirect |
| 6. #11763033 | C2 | semidirect |
| 7. #11762970 | C2 | semidirect |
| 8. #11762948 | C2 | semidirect |
| 9. Q16×Dic17 | C2 | semidirect |
| 10. C8×C22⋊D17 | C2 | semidirect |
| 11. C22×Q16×C17 | C2 | semidirect |
| 58. Q16×C17 | D4 | semidirect |
| 114. C22×C17 | #135 | semidirect |
| 132. C22×Q16 | D17 | semidirect |
| 177. C17 | #3285 | semidirect |
| 195. Q16 | C22⋊D17 | semidirect |
| 256. C22 | #10587605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587605 | 2 |
| #11763470 | 2 |
| #11763194 | 2 |
| #11763047 | 2 |
| #11763045 | 2 |
| #11763033 | 2 |
| #11762970 | 2 |
| #11762948 | 2 |
| Q16×Dic17 | 2 |
| C8×C22⋊D17 | 2 |
| C22×Q16×C17 | 2 |
| #3285 | 17 |