Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668438 | C2 | semidirect |
| 2. #26041850 | C2 | semidirect |
| 4. #26041525 | C2 | semidirect |
| 5. #26041508 | C2 | semidirect |
| 6. #26041317 | C2 | semidirect |
| 7. #26041289 | C2 | semidirect |
| 8. #26041285 | C2 | semidirect |
| 9. C2×#131×C181 | C2 | semidirect |
| 20. #19153795 | C22 | semidirect |
| 25. #19153750 | C22 | semidirect |
| 26. #19153748 | C22 | semidirect |
| 27. #19153741 | C22 | semidirect |
| 32. C2×M16×C181 | C22 | semidirect |
| 34. C22×C8×C181 | C22 | semidirect |
| 67. C2×C8×C181 | D4 | semidirect |
| 120. C181 | #3057 | semidirect |
| 123. C2×#131 | D181 | semidirect |
| 139. C2×M16 | C2×D181 | semidirect |
| 141. C22×C8 | C2×D181 | semidirect |
| 179. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668438 | 2 |
| #26041850 | 2 |
| #26041843 | 2 |
| #26041525 | 2 |
| #26041508 | 2 |
| #26041317 | 2 |
| #26041289 | 2 |
| #26041285 | 2 |
| C2×#131×C181 | 2 |
| #3057 | 181 |