Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 2. #26042147 | C2 | direct (N × H) |
| 6. #19153895 | C4 | semidirect |
| 10. C2×C4×#10624382 | C4 | semidirect |
| 14. C2×#15668432 | C4 | semidirect |
| 16. C22×#13089678 | C4 | semidirect |
| 17. C22×C8×C181 | C4 | semidirect |
| 24. C4×#10624382 | C2×C4 | semidirect |
| 39. C2×#13089678 | C2×C4 | semidirect |
| 43. C2×C8×C181 | C2×C4 | semidirect |
| 91. C2×C181 | H(3,ℤ/4) | semidirect |
| 95. C181 | C2×H(3,ℤ/4) | semidirect |
| 106. C22×C8 | #10624382 | semidirect |
| 133. C2×C8 | C2×#10624382 | semidirect |
| 189. C2 | #26042147 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153895 | 2 |
| #26042147 | 2 |
| C22×#15668432 | 2 |
| C2×H(3,ℤ/4) | 181 |