Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. Q16×#595 | C2 | direct (N × H) |
| 15. C2×Q16×C17 | C4 | semidirect |
| 16. C2×#63231 | C4 | semidirect |
| 17. Q16×D17 | C4 | semidirect |
| 19. C2×Dic68 | C4 | semidirect |
| 45. Q16×C17 | C2×C4 | semidirect |
| 47. #63231 | C2×C4 | semidirect |
| 49. Dic68 | C2×C4 | semidirect |
| 56. C2×#595 | Q16 | direct (N × H) |
| 86. #595 | C2×Q16 | direct (N × H) |
| 99. C2×C17 | C4×Q16 | semidirect |
| 101. D17 | C4×Q16 | semidirect |
| 109. C2×Q16 | #595 | direct (N × H) |
| 121. C17 | C2×C4×Q16 | semidirect |
| 136. Q16 | C2×#595 | direct (N × H) |
| 193. C2 | Q16×#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 |
| Q16×#595 | 2 |
| C2×#10587534 | 2 |
| C2×#10587549 | 2 |
| C2×C8×#595 | 2 |
| C2×Q16×D17 | 2 |
| C2×C4×Q16 | 17 |