Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. M16×Dic181 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 7. #344×C181 | C2 | semidirect |
| 16. #19153734 | C4 | semidirect |
| 17. #19153732 | C4 | semidirect |
| 95. C181 | #1932 | semidirect |
| 102. #344 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041327 | 2 |
| #26041297 | 2 |
| C2×#19153742 | 2 |
| #26041261 | 2 |
| M16×Dic181 | 2 |
| #26041038 | 2 |
| #344×C181 | 2 |
| #1932 | 181 |