Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1736 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 581 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. #26041951 | C2 | direct (N × H) |
| 3. C2×#19153813 | C2 | semidirect |
| 4. C2×#19153791 | C2 | semidirect |
| 5. C2×C4×D724 | C2 | semidirect |
| 6. C2×C4×Q8×C181 | C2 | semidirect |
| 8. C2×#15668450 | C22 | semidirect |
| 13. #19153813 | C22 | semidirect |
| 14. #19153791 | C22 | semidirect |
| 15. C4×D724 | C22 | semidirect |
| 19. C4×Q8×C181 | C22 | semidirect |
| 35. C2×Q8×C181 | D4 | semidirect |
| 53. Q8×C181 | C2×D4 | semidirect |
| 56. C2×C4×C181 | #41 | semidirect |
| 70. C4×C181 | C2×#41 | semidirect |
| 72. C2×C181 | #550 | semidirect |
| 77. C181 | C2×#550 | semidirect |
| 83. C2×C4×Q8 | D181 | semidirect |
| 94. C4×Q8 | C2×D181 | semidirect |
| 102. C2×Q8 | D724 | semidirect |
| 125. Q8 | C2×D724 | semidirect |
| 134. C2×C4 | #15668450 | semidirect |
| 149. C4 | C2×#15668450 | semidirect |
| 151. C2 | #26041951 | 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 |
| #26041951 | 2 |
| C2×#19153813 | 2 |
| C2×#19153791 | 2 |
| C2×C4×D724 | 2 |
| C2×C4×Q8×C181 | 2 |
| C2×#550 | 181 |