Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
126 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 28. #15668424 | Q8 | semidirect |
| 59. C181 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic362 | 2 |
| #26041097 | 2 |
| #26041055 | 2 |
| #26041054 | 2 |
| C16×Dic181 | 2 |
| C4⋊C16×C181 | 2 |
| #2183 | 181 |