Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#19153781 | C2 | semidirect |
| 4. #26041184 | C2 | semidirect |
| 6. #26041169 | C2 | semidirect |
| 7. #26041150 | C2 | semidirect |
| 8. #26041125 | C2 | semidirect |
| 9. #384×C181 | C2 | semidirect |
| 13. #19153804 | C4 | semidirect |
| 33. C2×Dic362 | C2×C4 | semidirect |
| 46. #15668426 | C2×C4 | semidirect |
| 57. C42×C181 | C2×C4 | semidirect |
| 111. C181 | #2326 | semidirect |
| 120. #384 | D181 | semidirect |
| 169. C42 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| C2×#19153781 | 2 |
| C2×#19153778 | 2 |
| #26041184 | 2 |
| #26041180 | 2 |
| #26041169 | 2 |
| #26041150 | 2 |
| #26041125 | 2 |
| #384×C181 | 2 |
| #2326 | 181 |