Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 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. #11763213 | C2 | semidirect |
| 3. #11763143 | C2 | semidirect |
| 4. #11763142 | C2 | semidirect |
| 5. #11763102 | C2 | semidirect |
| 6. #11763047 | C2 | semidirect |
| 7. Q16×Dic17 | C2 | semidirect |
| 9. C2×#10587489 | C2 | semidirect |
| 10. #107×D17 | C2 | semidirect |
| 11. C17×#467 | C2 | semidirect |
| 79. C22⋊D17 | Q16 | semidirect |
| 118. #467 | D17 | semidirect |
| 155. C17 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763517 | 2 |
| #11763213 | 2 |
| #11763143 | 2 |
| #11763142 | 2 |
| #11763102 | 2 |
| #11763047 | 2 |
| Q16×Dic17 | 2 |
| C8×C22⋊D17 | 2 |
| C2×#10587489 | 2 |
| #107×D17 | 2 |
| C17×#467 | 2 |
| #3338 | 17 |