Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 6. #19153871 | C4 | semidirect |
| 13. C4×#13089678 | C4 | semidirect |
| 14. C4×C8×C181 | C4 | semidirect |
| 58. C181 | #1288 | semidirect |
| 70. C4×C8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042302 | 2 |
| #26042224 | 2 |
| C4×#15668432 | 2 |
| #1288 | 181 |