Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 2. #11763677 | C2 | semidirect |
| 8. #10587677 | C4 | semidirect |
| 11. C2×C4×#595 | C4 | semidirect |
| 12. C2×M16×C17 | C4 | semidirect |
| 13. C2×#63223 | C4 | semidirect |
| 17. C2×C8×D17 | C4 | semidirect |
| 35. C4×#595 | C2×C4 | semidirect |
| 37. C2×C8×C17 | C2×C4 | semidirect |
| 39. C2×#3622 | C2×C4 | semidirect |
| 97. D17 | H(3,ℤ/4) | semidirect |
| 103. C2×M16 | #595 | semidirect |
| 112. C17 | C2×H(3,ℤ/4) | semidirect |
| 131. C2×C8 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| #11763677 | 2 |
| C2×M16×D17 | 2 |
| C2×H(3,ℤ/4) | 17 |