Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #11762561 | C2 | semidirect |
| 4. Q8⋊#3622 | C2 | semidirect |
| 6. #11762531 | C2 | semidirect |
| 7. C17×#446 | C2 | semidirect |
| 74. #446 | D17 | semidirect |
| 100. C17 | #1585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63230 | 2 |
| C8×D68 | 2 |
| #11762561 | 2 |
| Q8⋊#3622 | 2 |
| #11762536 | 2 |
| #11762531 | 2 |
| C17×#446 | 2 |
| #1585 | 17 |