Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
156 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11763736 | C2 | semidirect |
| 4. #11763735 | C2 | semidirect |
| 14. C17×M32 | C4 | semidirect |
| 15. #10587483 | C4 | semidirect |
| 16. #10587469 | C4 | semidirect |
| 32. C16×C17 | C2×C4 | semidirect |
| 33. #63214 | C2×C4 | semidirect |
| 77. M32 | #595 | semidirect |
| 84. C17 | #2159 | semidirect |
| 100. C16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763819 | 2 |
| C2×#10587534 | 2 |
| #11763736 | 2 |
| #11763735 | 2 |
| M32×D17 | 2 |
| #2159 | 17 |