Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic1448 | C2 | semidirect |
| 4. C4×Dic724 | C2 | semidirect |
| 5. #26041084 | C2 | semidirect |
| 7. C4⋊C16×C181 | C2 | semidirect |
| 72. C181 | #2211 | semidirect |
| 78. C4⋊C16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1448 | 2 |
| C2×#19153761 | 2 |
| #26041663 | 2 |
| C4×Dic724 | 2 |
| #26041084 | 2 |
| #26041081 | 2 |
| C4⋊C16×C181 | 2 |
| #2211 | 181 |