Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26041607 | C2 | direct (N × H) |
| 3. C2×#19153747 | C2 | semidirect |
| 4. C2×#19153740 | C2 | semidirect |
| 13. #19153747 | C22 | semidirect |
| 14. #19153740 | C22 | semidirect |
| 83. C2×C181 | #483 | semidirect |
| 87. C181 | C2×#483 | semidirect |
| 171. C2 | #26041607 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic181 | 2 |
| #26041607 | 2 |
| C2×#19153747 | 2 |
| C2×#19153740 | 2 |
| C2×C22⋊#13089678 | 2 |
| C2×C22⋊Q8×C181 | 2 |
| C2×#483 | 181 |