Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×C4⋊Dic17 | C2 | semidirect |
| 4. #11762572 | C2 | semidirect |
| 5. C2×C4×C8×C17 | C2 | semidirect |
| 15. C4×D68 | C4 | semidirect |
| 18. #10587492 | C4 | direct (N × H) |
| 34. C2×C8×C17 | C2×C4 | semidirect |
| 41. C4⋊Dic17 | C2×C4 | semidirect |
| 66. D68 | C42 | semidirect |
| 81. C4×C17 | #102 | semidirect |
| 89. C2×C4×C8 | D17 | semidirect |
| 111. C17 | C4×#102 | semidirect |
| 127. C2×C8 | C4×D17 | semidirect |
| 175. C4 | #10587492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D68 | 2 |
| C2×#10587492 | 2 |
| C4×C4⋊Dic17 | 2 |
| #11762572 | 2 |
| C2×C4×C8×C17 | 2 |
| C4×#102 | 17 |