Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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. #26042251 | C2 | semidirect |
| 2. C4×C22⋊#10624382 | C2 | semidirect |
| 3. #26042131 | C2 | semidirect |
| 4. #26042130 | C2 | semidirect |
| 10. #19153873 | C22 | semidirect |
| 11. (C2×#10624382)⋊C4 | C22 | semidirect |
| 13. C2×D4×D181 | C4 | semidirect |
| 16. #19153790 | C4 | semidirect |
| 20. C4⋊C4×D181 | C4 | semidirect |
| 22. #121×C181 | C4 | semidirect |
| 122. C181 | #1507 | semidirect |
| 138. #121 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042251 | 2 |
| C4×C22⋊#10624382 | 2 |
| #26042131 | 2 |
| #26042130 | 2 |
| #121×D181 | 2 |
| #1507 | 181 |