Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763575 | C2 | semidirect |
| 3. #11762827 | C2 | semidirect |
| 4. #11762813 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #11762567 | C2 | semidirect |
| 7. C17×#344 | C2 | semidirect |
| 19. C2×D136 | C4 | semidirect |
| 20. C2×#63219 | C4 | semidirect |
| 112. #344 | D17 | semidirect |
| 137. C17 | #1903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| #11763575 | 2 |
| #11762827 | 2 |
| #11762813 | 2 |
| C2×#10587494 | 2 |
| #11762567 | 2 |
| C17×#344 | 2 |
| #1903 | 17 |