Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26041327 | C2 | semidirect |
| 5. #26041051 | C2 | semidirect |
| 6. #26041035 | C2 | semidirect |
| 7. #344×C181 | C2 | semidirect |
| 85. C181 | #2081 | semidirect |
| 92. #344 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041327 | 2 |
| #26041285 | 2 |
| #26041283 | 2 |
| C2×#19153732 | 2 |
| #26041051 | 2 |
| #26041035 | 2 |
| #344×C181 | 2 |
| #2081 | 181 |