Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
184 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 122 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. C4⋊#15668452 | C2 | direct (N × H) |
| 29. C2×C4×C181 | C16 | semidirect |
| 42. C4×C181 | C2×C16 | semidirect |
| 45. C2×C181 | C4⋊C16 | semidirect |
| 49. C181 | C2×C4⋊C16 | semidirect |
| 75. C2×C4 | #15668452 | semidirect |
| 92. C4 | C2×#15668452 | semidirect |
| 95. C2 | C4⋊#15668452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668452 | 2 |
| C4⋊#15668452 | 2 |
| C2×C4×#13089678 | 2 |
| C2×C4⋊C16 | 181 |