Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 7. #19153816 | C4 | semidirect |
| 24. C4⋊Dic181 | Q8 | semidirect |
| 67. C181 | #1987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153816 | 2 |
| C4×C4⋊Dic181 | 2 |
| #26041042 | 2 |
| C2×C4⋊C8×C181 | 2 |
| #1987 | 181 |