Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26041756 | C2 | semidirect |
| 4. #26041289 | C2 | semidirect |
| 6. #26041036 | C2 | semidirect |
| 7. #344×C181 | C2 | semidirect |
| 12. C2×Dic724 | C4 | semidirect |
| 13. C2×#15668438 | C4 | semidirect |
| 109. C181 | #1905 | semidirect |
| 116. #344 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| #26041756 | 2 |
| #26041295 | 2 |
| #26041289 | 2 |
| #26041252 | 2 |
| #26041036 | 2 |
| #344×C181 | 2 |
| #1905 | 181 |