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×#10587628 | C2 | semidirect |
| 3. #11763183 | C2 | semidirect |
| 4. #11763057 | C2 | semidirect |
| 5. #11763016 | C2 | semidirect |
| 6. #11763009 | C2 | semidirect |
| 7. #11762969 | C2 | semidirect |
| 8. #11762948 | C2 | semidirect |
| 9. C4×#63231 | C2 | semidirect |
| 10. #11762887 | C2 | semidirect |
| 11. D4×Q8×C17 | C2 | semidirect |
| 70. #63231 | D4 | semidirect |
| 127. C4×C17 | #137 | semidirect |
| 134. D4×Q8 | D17 | semidirect |
| 178. C17 | #3278 | semidirect |
| 265. C4 | #10587628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| #11763480 | 2 |
| #11763183 | 2 |
| #11763057 | 2 |
| #11763016 | 2 |
| #11763009 | 2 |
| #11762969 | 2 |
| #11762948 | 2 |
| C4×#63231 | 2 |
| #11762887 | 2 |
| D4×Q8×C17 | 2 |
| #3278 | 17 |