Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 2. #26041142 | C2 | direct (N × H) |
| 3. C2×#19153723 | C2 | semidirect |
| 8. #19153723 | C22 | semidirect |
| 11. C23×C4×C181 | C4 | semidirect |
| 27. C22×C4×C181 | C2×C4 | semidirect |
| 59. C2×C181 | #381 | semidirect |
| 63. C181 | C2×#381 | semidirect |
| 72. C23×C4 | Dic181 | semidirect |
| 90. C22×C4 | C2×Dic181 | semidirect |
| 123. C2 | #26041142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic181 | 2 |
| #26041142 | 2 |
| C2×#19153723 | 2 |
| C24×C4×C181 | 2 |
| C2×#381 | 181 |