Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. #11763683 | C2 | semidirect |
| 9. #10587677 | C4 | semidirect |
| 12. C2×C4⋊#595 | C4 | semidirect |
| 16. C2×M16×C17 | C4 | semidirect |
| 17. C2×#63223 | C4 | semidirect |
| 20. C2×#63218 | C4 | semidirect |
| 42. C4⋊#595 | C2×C4 | semidirect |
| 45. C2×C8×C17 | C2×C4 | semidirect |
| 47. C2×#3622 | C2×C4 | semidirect |
| 122. C2×M16 | #595 | semidirect |
| 133. C17 | #1736 | semidirect |
| 155. 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 |
| C22×C4⋊#595 | 2 |
| #11763683 | 2 |
| C2×M16×D17 | 2 |
| #1736 | 17 |