Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
166 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 5. #19153874 | C4 | semidirect |
| 7. C22×#13089678 | C4 | semidirect |
| 9. C2×M16×C181 | C4 | semidirect |
| 53. C181 | #1391 | semidirect |
| 58. C2×M16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042258 | 2 |
| #26041247 | 2 |
| #1391 | 181 |