Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11763673 | C2 | semidirect |
| 4. #11763672 | C2 | semidirect |
| 5. #11763671 | C2 | semidirect |
| 6. #11763670 | C2 | semidirect |
| 40. #63218 | C8 | semidirect |
| 58. C8×C17 | C2×C8 | semidirect |
| 60. #3622 | C2×C8 | semidirect |
| 100. C17 | #1565 | semidirect |
| 138. C8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763828 | 2 |
| #11763810 | 2 |
| #11763673 | 2 |
| #11763672 | 2 |
| #11763671 | 2 |
| #11763670 | 2 |
| #11762761 | 2 |
| #1565 | 17 |