Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 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. #11763849 | 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 |
| 44. Q16×C17 | C2×C4 | semidirect |
| 46. #63231 | C2×C4 | semidirect |
| 48. Dic68 | C2×C4 | semidirect |
| 94. C2×C17 | #441 | semidirect |
| 96. D17 | #441 | semidirect |
| 103. C2×Q16 | #595 | semidirect |
| 115. C17 | C2×#441 | semidirect |
| 129. Q16 | C2×#595 | semidirect |
| 181. C2 | #11763849 | 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 |
| #11763849 | 2 |
| C2×#10587533 | 2 |
| C2×#10587549 | 2 |
| C2×#10587532 | 2 |
| C2×Q16×D17 | 2 |
| C2×#441 | 17 |