Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153750 | C2 | semidirect |
| 3. #26041042 | C2 | semidirect |
| 11. C22×C8×C181 | C4 | semidirect |
| 49. C8×C181 | C22⋊C4 | semidirect |
| 54. C22×C181 | #107 | semidirect |
| 71. C181 | #1808 | semidirect |
| 79. C22×C8 | Dic181 | semidirect |
| 121. C8 | C22⋊Dic181 | semidirect |
| 126. C22 | #19153750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153750 | 2 |
| #26041139 | 2 |
| #26041042 | 2 |
| C23×C8×C181 | 2 |
| #1808 | 181 |