Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763214 | C2 | semidirect |
| 3. #11763151 | C2 | semidirect |
| 4. #11763095 | C2 | semidirect |
| 5. #11763050 | C2 | semidirect |
| 6. C4×Dic68 | C2 | semidirect |
| 7. #11762847 | C2 | semidirect |
| 110. C17 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763214 | 2 |
| #11763151 | 2 |
| #11763095 | 2 |
| #11763050 | 2 |
| C4×Dic68 | 2 |
| #11762847 | 2 |
| C8×D4×C17 | 2 |
| #3342 | 17 |