Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #11762847 | C2 | semidirect |
| 3. #11762637 | C2 | semidirect |
| 4. #11762635 | C2 | semidirect |
| 5. #11762611 | C2 | semidirect |
| 6. #11762611 | C2 | semidirect |
| 7. C17×C22⋊C16 | C2 | semidirect |
| 71. C22⋊C16 | D17 | semidirect |
| 88. C17 | #2234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763045 | 2 |
| #11762847 | 2 |
| #11762637 | 2 |
| #11762635 | 2 |
| #11762611 | 2 |
| C17×C22⋊C16 | 2 |
| #2234 | 17 |