Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19153739 | C2 | semidirect |
| 3. C2×#19153739 | C2 | semidirect |
| 6. #26041034 | C2 | semidirect |
| 7. #389×C181 | C2 | semidirect |
| 129. C181 | #2042 | semidirect |
| 136. #389 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| C2×#19153739 | 2 |
| C2×#19153736 | 2 |
| #26041034 | 2 |
| #389×C181 | 2 |
| #2042 | 181 |