Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 29. #15668439 | C8 | semidirect |
| 44. #13089685 | Q16 | semidirect |
| 71. C181 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042328 | 2 |
| Q8×#13089685 | 2 |
| #26042143 | 2 |
| #26042129 | 2 |
| Q8⋊#13089685 | 2 |
| C8×#13089685 | 2 |
| #26041371 | 2 |
| C8×Q16 | 181 |