Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
296 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 9. #19153883 | C4 | semidirect |
| 11. C4×#13089685 | C4 | semidirect |
| 29. #15668428 | C8 | semidirect |
| 38. #13089685 | C4⋊C4 | semidirect |
| 64. Dic181 | C4×C8 | semidirect |
| 74. C181 | C8×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153883 | 2 |
| C2×C4×#13089685 | 2 |
| #26042145 | 2 |
| #26041130 | 2 |
| C8×C4⋊C4 | 181 |