Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#10587555 | C2 | semidirect |
| 3. #11763182 | C2 | semidirect |
| 4. #11763160 | C2 | semidirect |
| 5. #11763015 | C2 | semidirect |
| 6. #11762950 | C2 | semidirect |
| 7. C17×#431 | C2 | semidirect |
| 61. C2×C4×C17 | SD16 | semidirect |
| 102. #431 | D17 | semidirect |
| 129. C17 | #3206 | semidirect |
| 173. C2×C4 | #63219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| C2×#10587555 | 2 |
| #11763182 | 2 |
| #11763160 | 2 |
| #11763015 | 2 |
| #11762950 | 2 |
| C17×#431 | 2 |
| #3206 | 17 |