Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 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. #11763211 | C2 | semidirect |
| 3. #11763151 | C2 | semidirect |
| 4. #11763145 | C2 | semidirect |
| 5. #11763117 | C2 | semidirect |
| 6. #11763067 | C2 | semidirect |
| 7. C4×Dic68 | C2 | semidirect |
| 8. #11762851 | C2 | semidirect |
| 131. C17 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763499 | 2 |
| #11763211 | 2 |
| #11763151 | 2 |
| #11763145 | 2 |
| #11763117 | 2 |
| #11763067 | 2 |
| C4×Dic68 | 2 |
| #11762851 | 2 |
| C17×#436 | 2 |
| #3352 | 17 |