Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
166 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. Q8×#13089685 | C2 | semidirect |
| 3. #26042140 | C2 | semidirect |
| 4. Q8⋊#13089685 | C2 | semidirect |
| 6. #13089685⋊C8 | C2 | semidirect |
| 45. #13089685 | SD16 | semidirect |
| 56. Q8×C181 | M16 | semidirect |
| 77. C181 | #1583 | semidirect |
| 121. Q8 | #15668459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13089685 | 2 |
| #26042313 | 2 |
| #26042140 | 2 |
| Q8⋊#13089685 | 2 |
| #26042127 | 2 |
| #13089685⋊C8 | 2 |
| #26041364 | 2 |
| #1583 | 181 |