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×#10587604 | C2 | semidirect |
| 3. Q8×D68 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763056 | C2 | semidirect |
| 6. #11763019 | C2 | semidirect |
| 7. #11763009 | C2 | semidirect |
| 8. #11762974 | C2 | semidirect |
| 9. #11762949 | C2 | semidirect |
| 10. #11762888 | C2 | semidirect |
| 11. C4×Q16×C17 | C2 | semidirect |
| 59. Q16×C17 | D4 | semidirect |
| 127. C4×C17 | #137 | semidirect |
| 141. C4×Q16 | D17 | semidirect |
| 178. C17 | #3278 | semidirect |
| 197. Q16 | D68 | semidirect |
| 265. C4 | #10587604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587604 | 2 |
| #11763481 | 2 |
| Q8×D68 | 2 |
| #11763182 | 2 |
| #11763056 | 2 |
| #11763019 | 2 |
| #11763009 | 2 |
| #11762974 | 2 |
| #11762949 | 2 |
| #11762888 | 2 |
| C4×Q16×C17 | 2 |
| #3278 | 17 |