Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153838 | C2 | semidirect |
| 2. #26041715 | C2 | direct (N × H) |
| 3. C2×#19153760 | C2 | semidirect |
| 4. C2×#19153757 | C2 | semidirect |
| 5. C2×#19153756 | C2 | semidirect |
| 6. C22×D8×C181 | C2 | semidirect |
| 9. #19153838 | C22 | semidirect |
| 10. C2×Dic724 | C22 | semidirect |
| 12. C2×D1448 | C22 | semidirect |
| 13. #19153760 | C22 | semidirect |
| 14. #19153757 | C22 | semidirect |
| 15. #19153756 | C22 | semidirect |
| 16. C2×#15668424 | C22 | semidirect |
| 21. C2×D8×C181 | C22 | semidirect |
| 30. Dic724 | C23 | semidirect |
| 33. D1448 | C23 | semidirect |
| 34. #15668424 | C23 | semidirect |
| 84. C2×C181 | #509 | semidirect |
| 87. C181 | C2×#509 | semidirect |
| 90. C22×D8 | D181 | semidirect |
| 105. C2×D8 | C2×D181 | semidirect |
| 173. C2 | #26041715 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| #26041715 | 2 |
| C2×#19153760 | 2 |
| C2×#19153757 | 2 |
| C2×#19153756 | 2 |
| C22×D8×C181 | 2 |
| C2×#509 | 181 |