Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 11. #10587536 | C4 | semidirect |
| 12. #10587535 | C4 | semidirect |
| 17. C17×#108 | C4 | semidirect |
| 18. #10587493 | C4 | semidirect |
| 19. #10587490 | C4 | semidirect |
| 65. #595 | #108 | direct (N × H) |
| 88. #108 | #595 | direct (N × H) |
| 93. C17 | C4×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#108 | 2 |
| M16×#595 | 2 |
| C2×C8×#595 | 2 |
| #11763684 | 2 |
| #108×D17 | 2 |
| C4×#108 | 17 |