Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#19153844 | C2 | semidirect |
| 2. C2×#19153841 | C2 | semidirect |
| 3. #26041857 | C2 | semidirect |
| 4. C2×#19153744 | C2 | semidirect |
| 5. #26041181 | C2 | semidirect |
| 6. #26041047 | C2 | semidirect |
| 7. C2×#104×C181 | C2 | semidirect |
| 43. C2×D724 | D4 | semidirect |
| 53. #15668433 | D4 | semidirect |
| 72. M16×C181 | D4 | semidirect |
| 152. C181 | #2006 | semidirect |
| 158. C2×#104 | D181 | semidirect |
| 218. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C2×#19153841 | 2 |
| #26041857 | 2 |
| C2×#19153744 | 2 |
| #26041181 | 2 |
| #26041047 | 2 |
| C2×#104×C181 | 2 |
| #2006 | 181 |