Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19153731 | C2 | semidirect |
| 3. C2×#19153730 | C2 | semidirect |
| 4. #26041158 | C2 | semidirect |
| 5. #386×C181 | C2 | semidirect |
| 8. #19153861 | C4 | semidirect |
| 14. C2×C22⋊Dic181 | C22 | semidirect |
| 20. C23×C4×C181 | C22 | semidirect |
| 22. C2×C22⋊C4×C181 | C22 | semidirect |
| 70. C22×D181 | C22⋊C4 | semidirect |
| 84. C2×Dic181 | C22⋊C4 | semidirect |
| 92. C23×C181 | C22⋊C4 | semidirect |
| 110. C2×C4×C181 | C22⋊C4 | semidirect |
| 148. C181 | #1790 | semidirect |
| 154. #386 | D181 | semidirect |
| 164. C23×C4 | C2×D181 | semidirect |
| 168. C2×C22⋊C4 | C2×D181 | semidirect |
| 226. C23 | #15668426 | semidirect |
| 259. C2×C4 | #15668426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153861 | 2 |
| C2×#19153731 | 2 |
| C2×#19153730 | 2 |
| #26041158 | 2 |
| #386×C181 | 2 |
| #1790 | 181 |