Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #26041671 | C2 | semidirect |
| 3. #26041653 | C2 | semidirect |
| 4. #26041645 | C2 | semidirect |
| 5. #26041636 | C2 | semidirect |
| 6. #26041501 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041439 | C2 | semidirect |
| 9. #26041429 | C2 | semidirect |
| 10. #26041340 | C2 | semidirect |
| 11. #541×C181 | C2 | semidirect |
| 14. C2×#15668439 | C22 | semidirect |
| 17. C2×#15668436 | C22 | semidirect |
| 24. C4⋊#13089678 | C22 | semidirect |
| 25. #19153739 | C22 | semidirect |
| 28. #19153736 | C22 | semidirect |
| 30. #19153727 | C22 | semidirect |
| 31. C4×#13089678 | C22 | semidirect |
| 32. C4⋊Q8×C181 | C22 | semidirect |
| 35. #125×C181 | C22 | semidirect |
| 37. C4×Q8×C181 | C22 | semidirect |
| 122. C181 | #3222 | semidirect |
| 124. #541 | D181 | semidirect |
| 141. C4⋊Q8 | C2×D181 | semidirect |
| 146. #125 | C2×D181 | semidirect |
| 152. C4×Q8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041848 | 2 |
| #26041671 | 2 |
| #26041653 | 2 |
| #26041645 | 2 |
| #26041636 | 2 |
| #26041501 | 2 |
| #26041479 | 2 |
| #26041439 | 2 |
| #26041429 | 2 |
| #26041340 | 2 |
| #541×C181 | 2 |
| #3222 | 181 |