Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
820 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19153732 | C2 | semidirect |
| 3. #26041243 | C2 | semidirect |
| 4. #407×C181 | C2 | semidirect |
| 11. C2×#15668433 | C22 | semidirect |
| 15. C2×M16×C181 | C22 | semidirect |
| 67. C22×C181 | #100 | semidirect |
| 83. C181 | #1783 | semidirect |
| 88. #407 | D181 | semidirect |
| 97. C2×M16 | C2×D181 | semidirect |
| 156. C22 | #19153732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D724 | 2 |
| C2×#19153732 | 2 |
| #26041243 | 2 |
| #407×C181 | 2 |
| #1783 | 181 |