Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
316 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 213 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. C4⋊#13089678 | C4 | direct (N × H) |
| 23. C42×C181 | C8 | semidirect |
| 50. C4×C181 | C4×C8 | semidirect |
| 51. C4×C181 | C4⋊C8 | semidirect |
| 59. C181 | C4×C4⋊C8 | semidirect |
| 83. C42 | #13089678 | semidirect |
| 110. C4 | C4×#13089678 | semidirect |
| 111. C4 | C4⋊#13089678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13089678 | 2 |
| C2×C4×#13089678 | 2 |
| #26041034 | 2 |
| C43×C181 | 2 |
| C4×C4⋊C8 | 181 |