Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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×D1448 | C2 | semidirect |
| 2. C22×#15668432 | C2 | semidirect |
| 3. C2×#19153791 | C2 | semidirect |
| 4. #26041533 | C2 | direct (N × H) |
| 5. C2×#19153736 | C2 | semidirect |
| 6. C2×#106×C181 | C2 | semidirect |
| 11. C2×D1448 | C22 | semidirect |
| 13. C2×#15668432 | C22 | semidirect |
| 16. #19153791 | C22 | semidirect |
| 18. #19153736 | C22 | semidirect |
| 21. #106×C181 | C22 | semidirect |
| 42. C2×C8×C181 | D4 | semidirect |
| 70. C8×C181 | C2×D4 | semidirect |
| 86. C2×C181 | #469 | semidirect |
| 91. C181 | C2×#469 | semidirect |
| 97. C2×#106 | D181 | semidirect |
| 112. #106 | C2×D181 | semidirect |
| 133. C2×C8 | D724 | semidirect |
| 162. C8 | C2×D724 | semidirect |
| 180. C2 | #26041533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1448 | 2 |
| C22×#15668432 | 2 |
| C2×#19153791 | 2 |
| #26041533 | 2 |
| C2×#19153736 | 2 |
| C2×#106×C181 | 2 |
| C2×#469 | 181 |