Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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. C2×#19153846 | C2 | semidirect |
| 2. C2×#19153841 | C2 | semidirect |
| 3. C2×#19153804 | C2 | semidirect |
| 4. #26041671 | C2 | semidirect |
| 5. #26041666 | C2 | semidirect |
| 6. #26041661 | C2 | semidirect |
| 7. C4×#15668433 | C2 | semidirect |
| 8. #532×C181 | C2 | semidirect |
| 13. C2×#15668439 | C22 | semidirect |
| 14. C2×#15668437 | C22 | semidirect |
| 22. #19153727 | C22 | semidirect |
| 23. C4×#13089678 | C22 | semidirect |
| 25. C4⋊Q8×C181 | C22 | semidirect |
| 26. #127×C181 | C22 | semidirect |
| 27. #124×C181 | C22 | semidirect |
| 43. #15668433 | D4 | semidirect |
| 106. C181 | #3153 | semidirect |
| 110. #532 | D181 | semidirect |
| 126. C4⋊Q8 | C2×D181 | semidirect |
| 127. #127 | C2×D181 | semidirect |
| 131. #124 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153846 | 2 |
| C2×#19153841 | 2 |
| C2×#19153804 | 2 |
| #26041671 | 2 |
| #26041666 | 2 |
| #26041661 | 2 |
| C4×#15668433 | 2 |
| #532×C181 | 2 |
| #3153 | 181 |