Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #26041607 | C2 | semidirect |
| 3. #26041566 | C2 | semidirect |
| 4. #26041481 | C2 | semidirect |
| 6. C4×#15668436 | C2 | semidirect |
| 7. #26041332 | C2 | semidirect |
| 8. #533×C181 | C2 | semidirect |
| 18. #19153747 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 20. #19153740 | C22 | semidirect |
| 23. C4×#13089678 | C22 | semidirect |
| 24. C4⋊Q8×C181 | C22 | semidirect |
| 25. C4⋊Q8×C181 | C22 | semidirect |
| 30. C4×Q8×C181 | C22 | semidirect |
| 83. C2×C4×C181 | SD16 | semidirect |
| 112. C181 | #3101 | semidirect |
| 114. #533 | D181 | semidirect |
| 125. C4⋊Q8 | C2×D181 | semidirect |
| 126. C4⋊Q8 | C2×D181 | semidirect |
| 131. C4×Q8 | C2×D181 | semidirect |
| 195. C2×C4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D724 | 2 |
| #26041607 | 2 |
| #26041566 | 2 |
| #26041481 | 2 |
| #26041429 | 2 |
| C4×#15668436 | 2 |
| #26041332 | 2 |
| #533×C181 | 2 |
| #3101 | 181 |