Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11762849 | C2 | semidirect |
| 5. #11762570 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#428 | C2 | semidirect |
| 23. #10587494 | C4 | semidirect |
| 39. M16×C17 | C2×C4 | semidirect |
| 57. #63223 | C2×C4 | semidirect |
| 111. #428 | D17 | semidirect |
| 140. C17 | #1856 | semidirect |
| 156. M16 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763283 | 2 |
| #11762849 | 2 |
| C2×#10587494 | 2 |
| #11762710 | 2 |
| #11762570 | 2 |
| #11762568 | 2 |
| C17×#428 | 2 |
| #1856 | 17 |