Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 19. Dic724 | Q8 | direct (N × H) |
| 34. Q8×C181 | Q16 | semidirect |
| 50. C181 | Q8×Q16 | semidirect |
| 83. Q8 | Dic724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26041684 | 2 |
| #26041575 | 2 |
| C4×Dic724 | 2 |
| C8×Q8×C181 | 2 |
| Q8×Q16 | 181 |