Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C4×#13089685 | C2 | semidirect |
| 4. #26042145 | C2 | semidirect |
| 7. C2×D181⋊C8 | C4 | semidirect |
| 11. #19153873 | C4 | semidirect |
| 33. #15668426 | C8 | semidirect |
| 40. #13089685 | C22⋊C4 | semidirect |
| 48. C2×Dic181 | C2×C8 | semidirect |
| 61. C2×C4×C181 | C2×C8 | semidirect |
| 71. C2×D181 | C4×C8 | semidirect |
| 84. C181 | C8×C22⋊C4 | semidirect |
| 143. C2×C4 | D181⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D181⋊C8 | 2 |
| C2×#19153873 | 2 |
| C2×C4×#13089685 | 2 |
| #26042145 | 2 |
| #26041126 | 2 |
| C8×C22⋊C4 | 181 |