Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C22⋊#13089678 | C2 | semidirect |
| 2. #26041003 | C2 | direct (N × H) |
| 6. C22⋊#13089678 | C22 | semidirect |
| 21. C24×C181 | C8 | semidirect |
| 53. C23×C181 | C2×C8 | semidirect |
| 93. C2×C181 | #323 | semidirect |
| 97. C181 | C2×#323 | semidirect |
| 117. C24 | #13089678 | semidirect |
| 150. C23 | C2×#13089678 | semidirect |
| 191. C2 | #26041003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13089678 | 2 |
| #26041003 | 2 |
| C22×C22⋊C4×C181 | 2 |
| C2×#323 | 181 |