Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #26041287 | C2 | semidirect |
| 5. #26041185 | C2 | semidirect |
| 6. #26041047 | C2 | semidirect |
| 7. #339×C181 | C2 | semidirect |
| 11. #19153849 | C4 | semidirect |
| 37. C2×Dic362 | C2×C4 | semidirect |
| 58. M16×C181 | C2×C4 | semidirect |
| 124. C181 | #1882 | semidirect |
| 132. #339 | D181 | semidirect |
| 177. M16 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| #26041759 | 2 |
| C2×#19153744 | 2 |
| #26041287 | 2 |
| #26041185 | 2 |
| #26041047 | 2 |
| #339×C181 | 2 |
| #1882 | 181 |