Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 20. C2×#13089678 | Q8 | semidirect |
| 23. C2×Q8×C181 | C8 | semidirect |
| 70. C181 | #1984 | semidirect |
| 89. C2×Q8 | #13089678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13089678 | 2 |
| C2×C4×#13089678 | 2 |
| #26041034 | 2 |
| C2×C4×Q8×C181 | 2 |
| #1984 | 181 |