Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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. C23×D724 | C2 | semidirect |
| 2. C23×D724 | C2 | semidirect |
| 3. C23×C4×D181 | C2 | semidirect |
| 4. C2×#19153791 | C2 | direct (N × H) |
| 5. C22×#15668426 | C2 | semidirect |
| 6. C22×C4⋊C4×C181 | C2 | semidirect |
| 11. C22×D724 | C22 | semidirect |
| 12. C22×D724 | C22 | semidirect |
| 15. C22×C4×D181 | C22 | semidirect |
| 16. #19153791 | C22 | direct (N × H) |
| 17. C2×#15668426 | C22 | semidirect |
| 20. C2×C4⋊C4×C181 | C22 | semidirect |
| 26. C23×D181 | D4 | semidirect |
| 31. C2×D724 | C23 | semidirect |
| 32. C2×D724 | C23 | semidirect |
| 36. C2×C4×D181 | C23 | semidirect |
| 37. #15668426 | C23 | semidirect |
| 40. C22×C4×C181 | D4 | semidirect |
| 43. C4⋊C4×C181 | C23 | semidirect |
| 51. C22×D181 | C2×D4 | semidirect |
| 64. C2×C4×C181 | C2×D4 | semidirect |
| 67. C22×C181 | #121 | semidirect |
| 79. C2×D181 | C22×D4 | semidirect |
| 81. C4×C181 | C22×D4 | semidirect |
| 83. C2×C181 | C2×#121 | semidirect |
| 89. C181 | C22×#121 | semidirect |
| 95. C22×C4⋊C4 | D181 | semidirect |
| 109. C2×C4⋊C4 | C2×D181 | semidirect |
| 129. C22×C4 | D724 | semidirect |
| 132. C4⋊C4 | C22×D181 | semidirect |
| 154. C2×C4 | C2×D724 | semidirect |
| 165. C22 | #19153791 | direct (N × H) |
| 172. C4 | C22×D724 | semidirect |
| 175. C2 | C2×#19153791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D724 | 2 |
| C23×C4×D181 | 2 |
| C2×#19153791 | 2 |
| C22×#15668426 | 2 |
| C22×C4⋊C4×C181 | 2 |
| C22×#121 | 181 |