Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×D724 | C2 | semidirect |
| 3. #26041182 | C2 | semidirect |
| 4. #26041180 | C2 | semidirect |
| 5. #26041158 | C2 | semidirect |
| 6. #26041155 | C2 | semidirect |
| 7. #26041144 | C2 | semidirect |
| 8. #26041125 | C2 | semidirect |
| 9. C2×C4×D4×C181 | C2 | semidirect |
| 13. #19153812 | C4 | semidirect |
| 33. C2×D724 | C2×C4 | semidirect |
| 36. C2×C22⋊D181 | C2×C4 | semidirect |
| 47. C4×Dic181 | C2×C4 | semidirect |
| 51. C2×D4×C181 | C2×C4 | semidirect |
| 60. C42×C181 | D4 | semidirect |
| 123. C181 | #2328 | semidirect |
| 127. C2×C4×D4 | D181 | semidirect |
| 164. C2×D4 | C4×D181 | semidirect |
| 184. C42 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153812 | 2 |
| C2×C4×D724 | 2 |
| #26041182 | 2 |
| #26041180 | 2 |
| #26041158 | 2 |
| #26041155 | 2 |
| #26041144 | 2 |
| #26041125 | 2 |
| C2×C4×D4×C181 | 2 |
| #2328 | 181 |