Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic362 | C2 | semidirect |
| 3. #26041184 | C2 | semidirect |
| 5. #26041167 | C2 | semidirect |
| 6. #26041152 | C2 | semidirect |
| 7. #26041148 | C2 | semidirect |
| 8. #26041125 | C2 | semidirect |
| 11. #19153803 | C4 | semidirect |
| 32. C2×Dic362 | C2×C4 | semidirect |
| 41. C22⋊Dic181 | C2×C4 | semidirect |
| 44. C4×Dic181 | C2×C4 | semidirect |
| 111. C181 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153803 | 2 |
| C2×C4×Dic362 | 2 |
| #26041184 | 2 |
| #26041182 | 2 |
| #26041167 | 2 |
| #26041152 | 2 |
| #26041148 | 2 |
| #26041125 | 2 |
| C2×C4×D4×C181 | 2 |
| #2326 | 181 |