Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
524 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#19153808 | C2 | semidirect |
| 2. #26041186 | C2 | semidirect |
| 4. #26041173 | C2 | semidirect |
| 5. C42×Dic181 | C2 | semidirect |
| 68. C181 | #2861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153808 | 2 |
| #26041186 | 2 |
| #26041182 | 2 |
| #26041173 | 2 |
| C42×Dic181 | 2 |
| C2×#124×C181 | 2 |
| #2861 | 181 |