Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
880 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#19153875 | C2 | semidirect |
| 2. C2×#19153874 | C2 | semidirect |
| 3. #26042220 | C2 | semidirect |
| 6. C2×C22⋊#10624382 | C22 | semidirect |
| 9. C24×D181 | C4 | semidirect |
| 12. C22×C22⋊D181 | C4 | semidirect |
| 17. C22×C4×D181 | C4 | semidirect |
| 18. C22×D4×C181 | C4 | semidirect |
| 74. C22×D181 | C22⋊C4 | semidirect |
| 83. C2×Dic181 | C22⋊C4 | semidirect |
| 92. C23×C181 | C22⋊C4 | semidirect |
| 97. C2×C4×C181 | C22⋊C4 | semidirect |
| 123. C2×D181 | #99 | semidirect |
| 137. C181 | #1781 | semidirect |
| 151. C22×D4 | #10624382 | semidirect |
| 221. C23 | C22⋊#10624382 | semidirect |
| 235. C2×C4 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153875 | 2 |
| C2×#19153874 | 2 |
| #26042220 | 2 |
| C22×D4×D181 | 2 |
| #1781 | 181 |