Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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×#15668450 | C2 | semidirect |
| 2. C22×Q8×D181 | C2 | semidirect |
| 3. #26041941 | C2 | direct (N × H) |
| 4. C2×#19153804 | C2 | semidirect |
| 5. C2×#19153796 | C2 | semidirect |
| 6. C2×#19153791 | C2 | semidirect |
| 7. C2×C4×D724 | C2 | semidirect |
| 8. C2×C4×Q8×C181 | C2 | semidirect |
| 10. C2×#15668450 | C22 | semidirect |
| 13. C2×Q8×D181 | C22 | semidirect |
| 18. #19153804 | C22 | semidirect |
| 19. #19153796 | C22 | semidirect |
| 20. #19153791 | C22 | semidirect |
| 21. C4×D724 | C22 | semidirect |
| 27. C4×Q8×C181 | C22 | semidirect |
| 50. C2×Q8×C181 | D4 | semidirect |
| 62. C22×D181 | #41 | semidirect |
| 75. Q8×C181 | C2×D4 | semidirect |
| 93. C2×D181 | C2×#41 | semidirect |
| 99. C2×C181 | #548 | semidirect |
| 105. C181 | C2×#548 | semidirect |
| 113. C2×C4×Q8 | D181 | semidirect |
| 128. C4×Q8 | C2×D181 | semidirect |
| 142. C2×Q8 | D724 | semidirect |
| 173. Q8 | C2×D724 | semidirect |
| 207. C2 | #26041941 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668450 | 2 |
| C22×Q8×D181 | 2 |
| #26041941 | 2 |
| C2×#19153804 | 2 |
| C2×#19153796 | 2 |
| C2×#19153791 | 2 |
| C2×C4×D724 | 2 |
| C2×C4×Q8×C181 | 2 |
| C2×#548 | 181 |