Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 10. C4×#3624 | C4 | semidirect |
| 11. #10587532 | C4 | direct (N × H) |
| 12. C4×C8×C17 | C4 | semidirect |
| 13. C8×Dic17 | C4 | semidirect |
| 14. C4×#3622 | C4 | semidirect |
| 37. #3624 | C42 | semidirect |
| 38. C8×C17 | C42 | semidirect |
| 39. #3622 | C42 | semidirect |
| 45. C4×C17 | #97 | semidirect |
| 47. Dic17 | #97 | semidirect |
| 65. C4×C8 | #595 | semidirect |
| 66. C17 | C4×#97 | semidirect |
| 91. C8 | C4×#595 | semidirect |
| 98. C4 | #10587532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587532 | 2 |
| C4×#63242 | 2 |
| C42×#595 | 2 |
| C4×C8×D17 | 2 |
| C4×#97 | 17 |