Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
564 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 13. C2×C4⋊C4×C17 | C4 | semidirect |
| 14. C2×C4⋊Dic17 | C4 | semidirect |
| 15. C2×#63225 | C4 | semidirect |
| 16. C2×#63225 | C4 | semidirect |
| 93. C2×C4×C17 | C4⋊C4 | semidirect |
| 100. C2×Dic17 | C4⋊C4 | semidirect |
| 171. C2×C4⋊C4 | #595 | semidirect |
| 175. C17 | #1441 | semidirect |
| 263. C2×C4 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C2×C4⋊C4×D17 | 2 |
| #1441 | 17 |