Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153823 | C2 | semidirect |
| 4. #26041527 | C2 | semidirect |
| 5. #26041510 | C2 | semidirect |
| 6. #26041315 | C2 | semidirect |
| 7. #26041288 | C2 | semidirect |
| 8. #26041283 | C2 | semidirect |
| 9. #536×C181 | C2 | semidirect |
| 16. C2×#15668433 | C22 | semidirect |
| 18. C22×#13089678 | C22 | semidirect |
| 24. #19153749 | C22 | semidirect |
| 25. #19153747 | C22 | semidirect |
| 26. #19153740 | C22 | semidirect |
| 33. C22⋊Q8×C181 | C22 | semidirect |
| 46. C2×#13089678 | D4 | semidirect |
| 120. C181 | #3057 | semidirect |
| 124. #536 | D181 | semidirect |
| 147. C22⋊Q8 | 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×#19153823 | 2 |
| #26041843 | 2 |
| #26041527 | 2 |
| #26041510 | 2 |
| #26041315 | 2 |
| #26041288 | 2 |
| #26041283 | 2 |
| #536×C181 | 2 |
| #3057 | 181 |