Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 3. #26041107 | C2 | semidirect |
| 4. #26041083 | C2 | semidirect |
| 5. C2×Q32×C181 | C2 | semidirect |
| 51. C181 | #2219 | semidirect |
| 53. C2×Q32 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153755 | 2 |
| #26041517 | 2 |
| #26041107 | 2 |
| #26041083 | 2 |
| C2×Q32×C181 | 2 |
| #2219 | 181 |