Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C42×Dic17 | C2 | semidirect |
| 5. #11762570 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 11. Q8×Dic17 | C4 | semidirect |
| 13. D4×Dic17 | C4 | semidirect |
| 21. C17×#104 | C4 | semidirect |
| 22. #10587508 | C4 | semidirect |
| 39. M16×C17 | C2×C4 | semidirect |
| 42. C42×C17 | C2×C4 | semidirect |
| 52. C4×Dic17 | C2×C4 | semidirect |
| 56. #63223 | C2×C4 | semidirect |
| 61. Q8×C17 | C42 | semidirect |
| 65. D4×C17 | C42 | semidirect |
| 102. Dic17 | #104 | direct (N × H) |
| 129. #104 | Dic17 | direct (N × H) |
| 132. C17 | C4×#104 | semidirect |
| 149. M16 | C2×Dic17 | semidirect |
| 165. C42 | C2×Dic17 | semidirect |
| 169. Q8 | C4×Dic17 | semidirect |
| 173. D4 | C4×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic17 | 2 |
| C2×#10587508 | 2 |
| M16×Dic17 | 2 |
| C42×Dic17 | 2 |
| #11762570 | 2 |
| #11762569 | 2 |
| C2×C17×#104 | 2 |
| C4×#104 | 17 |