Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19153804 | C2 | semidirect |
| 2. C2×#19153795 | C2 | semidirect |
| 4. #26041185 | C2 | semidirect |
| 5. #26041181 | C2 | semidirect |
| 6. #26041170 | C2 | semidirect |
| 7. #26041158 | C2 | semidirect |
| 8. #26041145 | C2 | semidirect |
| 9. C22×C42×C181 | C2 | semidirect |
| 63. C42×C181 | D4 | semidirect |
| 103. C22×C181 | #124 | semidirect |
| 128. C181 | #2850 | semidirect |
| 133. C22×C42 | D181 | semidirect |
| 192. C42 | C22⋊D181 | semidirect |
| 237. C22 | #19153804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| C2×#19153795 | 2 |
| C2×#19153790 | 2 |
| #26041185 | 2 |
| #26041181 | 2 |
| #26041170 | 2 |
| #26041158 | 2 |
| #26041145 | 2 |
| C22×C42×C181 | 2 |
| #2850 | 181 |