Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
338 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19153734 | C2 | semidirect |
| 4. #26041047 | C2 | semidirect |
| 88. C22×C181 | #101 | semidirect |
| 104. C181 | #1901 | semidirect |
| 193. C22 | #19153734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668433 | 2 |
| C2×#19153795 | 2 |
| C2×#19153734 | 2 |
| #26041047 | 2 |
| #407×C181 | 2 |
| #1901 | 181 |