Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
110 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 110 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 |
|---|---|---|
| 1. C4⋊#15668452 | C2 | semidirect |
| 2. C4×#15668452 | C2 | semidirect |
| 29. D4×C181 | C16 | semidirect |
| 50. C181 | D4⋊C16 | semidirect |
| 76. D4 | #15668452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊#15668452 | 2 |
| C4×#15668452 | 2 |
| D4×#13089678 | 2 |
| D4⋊C16 | 181 |