Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11763009 | C2 | semidirect |
| 3. Q8×#3622 | C2 | semidirect |
| 4. #11762561 | C2 | semidirect |
| 5. #11762553 | C2 | semidirect |
| 6. #11762552 | C2 | semidirect |
| 7. C17×#460 | C2 | semidirect |
| 46. Q8×C17 | D8 | semidirect |
| 66. #3622 | SD16 | semidirect |
| 84. #460 | D17 | semidirect |
| 109. C17 | #1668 | semidirect |
| 133. Q8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763185 | 2 |
| #11763009 | 2 |
| Q8×#3622 | 2 |
| #11762561 | 2 |
| #11762553 | 2 |
| #11762552 | 2 |
| C17×#460 | 2 |
| #1668 | 17 |