Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #26041235 | C2 | semidirect |
| 4. C2×C8×Dic181 | C2 | semidirect |
| 5. #26041044 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 9. #19153823 | C4 | semidirect |
| 16. #19153743 | C4 | semidirect |
| 23. #103×C181 | C4 | semidirect |
| 24. #102×C181 | C4 | semidirect |
| 98. C181 | #1764 | semidirect |
| 119. #103 | Dic181 | semidirect |
| 120. #102 | Dic181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153823 | 2 |
| C2×#19153743 | 2 |
| #26041235 | 2 |
| C2×C8×Dic181 | 2 |
| #26041044 | 2 |
| #26041038 | 2 |
| #416×C181 | 2 |
| #1764 | 181 |