Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 412 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. C2×#19153871 | C2 | semidirect |
| 3. #26042145 | C2 | semidirect |
| 6. C22⋊#13089685 | C4 | semidirect |
| 18. C2×#13089685 | C2×C4 | semidirect |
| 75. C22×C181 | #97 | semidirect |
| 97. C181 | #1749 | semidirect |
| 173. C22 | #19153871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13089685 | 2 |
| C2×#19153871 | 2 |
| #26042145 | 2 |
| C22×C4×Dic181 | 2 |
| #1749 | 181 |