Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C22×#15668449 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. C2×#19153790 | C2 | semidirect |
| 4. #26041426 | C2 | semidirect |
| 5. #26041420 | C2 | semidirect |
| 6. #26041415 | C2 | semidirect |
| 7. #26041281 | C2 | semidirect |
| 8. #407×C181 | C2 | semidirect |
| 13. C2×#15668449 | C22 | semidirect |
| 14. C22×Dic362 | C22 | semidirect |
| 15. C22×D724 | C22 | semidirect |
| 16. C22×D724 | C22 | semidirect |
| 21. C2×#15668438 | C22 | semidirect |
| 22. C2×D1448 | C22 | semidirect |
| 26. #19153790 | C22 | semidirect |
| 27. C2×C4⋊Dic181 | C22 | semidirect |
| 29. #19153741 | C22 | semidirect |
| 30. #19153738 | C22 | semidirect |
| 32. C2×M16×C181 | C22 | semidirect |
| 33. C22⋊C8×C181 | C22 | semidirect |
| 34. C22⋊C8×C181 | C22 | semidirect |
| 42. #15668449 | D4 | semidirect |
| 89. Dic362 | C2×D4 | semidirect |
| 94. D724 | C2×D4 | semidirect |
| 131. C22×C181 | AGL(1,ℤ/8) | semidirect |
| 155. C181 | #3006 | semidirect |
| 164. #407 | D181 | semidirect |
| 180. C2×M16 | C2×D181 | semidirect |
| 189. C22⋊C8 | C2×D181 | semidirect |
| 190. C22⋊C8 | C2×D181 | semidirect |
| 295. C22 | #19153844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668449 | 2 |
| C2×#19153844 | 2 |
| C2×#19153790 | 2 |
| #26041426 | 2 |
| #26041420 | 2 |
| #26041415 | 2 |
| #26041281 | 2 |
| #407×C181 | 2 |
| #3006 | 181 |