Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 304 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. C22⋊C8×D181 | C2 | semidirect |
| 3. #26041126 | C2 | semidirect |
| 4. #26041017 | C2 | semidirect |
| 5. #26041015 | C2 | semidirect |
| 6. #26041013 | C2 | semidirect |
| 7. #327×C181 | C2 | semidirect |
| 8. C2×#15668448 | C4 | semidirect |
| 12. #19153796 | C4 | semidirect |
| 14. #19153787 | C4 | semidirect |
| 18. #19153774 | C4 | semidirect |
| 128. C181 | #1501 | semidirect |
| 136. #327 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041789 | 2 |
| C22⋊C8×D181 | 2 |
| #26041126 | 2 |
| #26041017 | 2 |
| #26041015 | 2 |
| #26041013 | 2 |
| #327×C181 | 2 |
| #1501 | 181 |