Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 3. #26042285 | C2 | direct (N × H) |
| 4. C2×#19153883 | C2 | semidirect |
| 5. C2×C4⋊#13089685 | C2 | semidirect |
| 14. #19153883 | C22 | semidirect |
| 15. C4⋊#13089685 | C22 | semidirect |
| 78. C2×C181 | #424 | semidirect |
| 81. C181 | C2×#424 | semidirect |
| 160. C2 | #26042285 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668458 | 2 |
| C23×#13089685 | 2 |
| #26042285 | 2 |
| C2×#19153883 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×#19153772 | 2 |
| C2×#424 | 181 |