Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 9. #10587544 | C4 | semidirect |
| 12. C17×C4⋊C8 | C4 | semidirect |
| 14. C4⋊#3622 | C4 | semidirect |
| 80. C4⋊C8 | #595 | semidirect |
| 84. C17 | #1303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763827 | 2 |
| C4×C4⋊#595 | 2 |
| #11762831 | 2 |
| #1303 | 17 |