Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26041303 | C2 | semidirect |
| 3. C2×#19153744 | C2 | semidirect |
| 4. #26041263 | C2 | semidirect |
| 5. #26041261 | C2 | semidirect |
| 6. #26041037 | C2 | semidirect |
| 7. C2×#104×C181 | C2 | semidirect |
| 122. C181 | #2050 | semidirect |
| 127. C2×#104 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| #26041303 | 2 |
| C2×#19153744 | 2 |
| #26041263 | 2 |
| #26041261 | 2 |
| #26041037 | 2 |
| C2×#104×C181 | 2 |
| #2050 | 181 |