Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763103 | C2 | semidirect |
| 3. #11763102 | C2 | semidirect |
| 6. #11763018 | C2 | semidirect |
| 7. #11763017 | C2 | semidirect |
| 76. C2×Dic17 | Q16 | semidirect |
| 137. C17 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763361 | 2 |
| #11763103 | 2 |
| #11763102 | 2 |
| #11763050 | 2 |
| #11763048 | 2 |
| #11763018 | 2 |
| #11763017 | 2 |
| C2×#10587485 | 2 |
| C17×#467 | 2 |
| #3249 | 17 |