Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 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. C22×#15668436 | C2 | semidirect |
| 2. C2×#19153824 | C2 | semidirect |
| 3. #26041853 | C2 | semidirect |
| 5. #26041528 | C2 | semidirect |
| 6. #26041511 | C2 | semidirect |
| 7. #26041315 | C2 | semidirect |
| 8. #26041285 | C2 | semidirect |
| 9. #419×C181 | C2 | semidirect |
| 16. C2×#15668432 | C22 | semidirect |
| 18. C2×C8×D181 | C22 | semidirect |
| 24. #19153792 | C22 | semidirect |
| 28. #19153749 | C22 | semidirect |
| 29. #19153747 | C22 | semidirect |
| 34. #103×C181 | C22 | semidirect |
| 50. C2×#13089678 | D4 | semidirect |
| 120. C181 | #3057 | semidirect |
| 129. #419 | D181 | semidirect |
| 154. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| C2×#19153824 | 2 |
| #26041853 | 2 |
| #26041848 | 2 |
| #26041528 | 2 |
| #26041511 | 2 |
| #26041315 | 2 |
| #26041285 | 2 |
| #419×C181 | 2 |
| #3057 | 181 |