Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. M16×Dic17 | C2 | semidirect |
| 4. #11762578 | C2 | semidirect |
| 5. C17×#343 | C2 | semidirect |
| 15. #10587494 | C4 | semidirect |
| 31. M16×C17 | C2×C4 | semidirect |
| 38. #63223 | C2×C4 | semidirect |
| 79. Dic17 | #100 | semidirect |
| 84. #343 | D17 | semidirect |
| 103. C17 | C4×#100 | semidirect |
| 119. M16 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587579 | 2 |
| C2×#10587494 | 2 |
| M16×Dic17 | 2 |
| #11762578 | 2 |
| C17×#343 | 2 |
| C4×#100 | 17 |