Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
164 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 26. Q16×C17 | C8 | semidirect |
| 27. #63231 | C8 | semidirect |
| 28. Dic68 | C8 | semidirect |
| 36. #3633 | Q16 | direct (N × H) |
| 73. C17 | C8×Q16 | semidirect |
| 77. Q16 | #3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3633 | 2 |
| #11763899 | 2 |
| Q8⋊#3633 | 2 |
| C8×#3633 | 2 |
| Q16×#595 | 2 |
| C8×Q16 | 17 |