Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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 |
|---|---|---|
| 6. C2×#63243 | C4 | semidirect |
| 7. C2×#63242 | C4 | semidirect |
| 13. C17×#101 | C4 | semidirect |
| 14. #10587507 | C4 | semidirect |
| 86. #101 | #595 | semidirect |
| 92. C17 | #1395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763790 | 2 |
| #11763784 | 2 |
| #11762792 | 2 |
| #1395 | 17 |