Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19153815 | C2 | semidirect |
| 3. #26041676 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041598 | C2 | semidirect |
| 6. #26041597 | C2 | semidirect |
| 7. #26041595 | C2 | semidirect |
| 8. #26041568 | C2 | semidirect |
| 9. #26041567 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #481×C181 | C2 | semidirect |
| 137. C181 | #3227 | semidirect |
| 146. #481 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×#19153815 | 2 |
| #26041676 | 2 |
| #26041624 | 2 |
| #26041598 | 2 |
| #26041597 | 2 |
| #26041595 | 2 |
| #26041568 | 2 |
| #26041567 | 2 |
| #26041329 | 2 |
| #481×C181 | 2 |
| #3227 | 181 |