Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
684 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 320 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 |
|---|---|---|
| 7. Q8×#595 | C4 | direct (N × H) |
| 13. C4×Q8×C17 | C4 | semidirect |
| 14. Q8×Dic17 | C4 | semidirect |
| 16. #10587573 | C4 | semidirect |
| 18. C4×Dic34 | C4 | semidirect |
| 32. C4×#595 | Q8 | direct (N × H) |
| 47. Q8×C17 | C42 | semidirect |
| 58. Dic34 | C42 | semidirect |
| 66. #595 | C4×Q8 | direct (N × H) |
| 69. C4×C17 | C4×Q8 | semidirect |
| 72. Dic17 | C4×Q8 | semidirect |
| 88. C4×Q8 | #595 | direct (N × H) |
| 97. C17 | C42×Q8 | semidirect |
| 120. Q8 | C4×#595 | direct (N × H) |
| 149. C4 | Q8×#595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| C4⋊C4×#595 | 2 |
| C4×C4⋊#595 | 2 |
| C42×#595 | 2 |
| C4×Q8×D17 | 2 |
| C42×Q8 | 17 |