Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. #11762570 | C2 | semidirect |
| 5. #11762569 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 7. C17×#339 | C2 | semidirect |
| 18. M16×D17 | C4 | semidirect |
| 21. #10587578 | C4 | semidirect |
| 22. C4⋊C4×D17 | C4 | semidirect |
| 27. #10587558 | C4 | semidirect |
| 44. M16×C17 | C2×C4 | semidirect |
| 50. C42×C17 | C2×C4 | semidirect |
| 60. C4×Dic17 | C2×C4 | semidirect |
| 62. #63223 | C2×C4 | semidirect |
| 126. #339 | D17 | semidirect |
| 154. C17 | #1733 | semidirect |
| 173. M16 | C4×D17 | semidirect |
| 191. C42 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D17 | 2 |
| C2×#10587558 | 2 |
| #117×D17 | 2 |
| #11762570 | 2 |
| #11762569 | 2 |
| #11762568 | 2 |
| C17×#339 | 2 |
| #1733 | 17 |