Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19153839 | C2 | semidirect |
| 2. C2×#19153835 | C2 | semidirect |
| 3. #26041710 | C2 | direct (N × H) |
| 4. C2×#19153762 | C2 | semidirect |
| 5. C2×#19153761 | C2 | semidirect |
| 6. C2×#19153757 | C2 | semidirect |
| 7. C2×C16×D181 | C2 | semidirect |
| 8. C2×SD32×C181 | C2 | semidirect |
| 12. #19153839 | C22 | semidirect |
| 14. #19153835 | C22 | semidirect |
| 20. #19153762 | C22 | semidirect |
| 21. #19153761 | C22 | semidirect |
| 22. #19153757 | C22 | semidirect |
| 24. C16×D181 | C22 | semidirect |
| 27. SD32×C181 | C22 | semidirect |
| 95. C2×C181 | #508 | semidirect |
| 99. C181 | C2×#508 | semidirect |
| 106. C2×SD32 | D181 | semidirect |
| 124. SD32 | C2×D181 | semidirect |
| 197. C2 | #26041710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×#19153835 | 2 |
| #26041710 | 2 |
| C2×#19153762 | 2 |
| C2×#19153761 | 2 |
| C2×#19153757 | 2 |
| C2×C16×D181 | 2 |
| C2×SD32×C181 | 2 |
| C2×#508 | 181 |