Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
166 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 5. C2×#63247 | C4 | semidirect |
| 6. C22×#3624 | C4 | semidirect |
| 11. #10587551 | C4 | semidirect |
| 13. C17×#99 | C4 | semidirect |
| 14. #10587505 | C4 | semidirect |
| 91. #99 | #595 | semidirect |
| 94. C17 | #1391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763789 | 2 |
| #11763782 | 2 |
| #11762781 | 2 |
| #1391 | 17 |