Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
880 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 94 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. #26042220 | C2 | semidirect |
| 5. C2×C22⋊#10624382 | C22 | semidirect |
| 7. C24×D181 | C4 | semidirect |
| 11. C22×D724 | C4 | semidirect |
| 13. C23×C4×C181 | C4 | semidirect |
| 54. C22×D181 | C22⋊C4 | semidirect |
| 66. C2×C4×C181 | C22⋊C4 | semidirect |
| 71. C22×C181 | #99 | semidirect |
| 95. C181 | #1781 | semidirect |
| 106. C23×C4 | #10624382 | semidirect |
| 162. C2×C4 | C22⋊#10624382 | semidirect |
| 179. C22 | #19153875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153875 | 2 |
| #26042220 | 2 |
| C23×D724 | 2 |
| #1781 | 181 |