Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 8. C22⋊#13089685 | C4 | semidirect |
| 11. C2×#15668433 | C4 | semidirect |
| 14. C2×M16×C181 | C4 | semidirect |
| 87. C181 | #1305 | semidirect |
| 95. C2×M16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042250 | 2 |
| #26042221 | 2 |
| #26041242 | 2 |
| #1305 | 181 |