Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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 |
|---|---|---|
| 2. Q32×D181 | C2 | semidirect |
| 3. #26041119 | C2 | semidirect |
| 4. #26041118 | C2 | semidirect |
| 5. #26041116 | C2 | semidirect |
| 6. #26041112 | C2 | semidirect |
| 7. Q64×C181 | C2 | semidirect |
| 51. C181 | #2264 | semidirect |
| 56. Q64 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041712 | 2 |
| Q32×D181 | 2 |
| #26041119 | 2 |
| #26041118 | 2 |
| #26041116 | 2 |
| #26041112 | 2 |
| Q64×C181 | 2 |
| #2264 | 181 |