Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19153745 | C2 | semidirect |
| 3. C2×#19153741 | C2 | semidirect |
| 4. C2×#19153739 | C2 | semidirect |
| 6. C4⋊C4×Dic181 | C2 | semidirect |
| 11. #19153803 | C4 | semidirect |
| 130. C181 | #1983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153803 | 2 |
| C2×#19153745 | 2 |
| C2×#19153741 | 2 |
| C2×#19153739 | 2 |
| C2×#19153737 | 2 |
| C4⋊C4×Dic181 | 2 |
| C2×#102×C181 | 2 |
| #1983 | 181 |