Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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. D181⋊(C22⋊C8) | C2 | semidirect |
| 2. C4×C22⋊#10624382 | C2 | semidirect |
| 3. #26042133 | C2 | semidirect |
| 4. #26042130 | C2 | semidirect |
| 14. #19153792 | C4 | semidirect |
| 16. #19153787 | C4 | semidirect |
| 21. #19153775 | C4 | semidirect |
| 22. C2×#41×C181 | C4 | semidirect |
| 112. C181 | #1501 | semidirect |
| 119. C2×#41 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊(C22⋊C8) | 2 |
| C4×C22⋊#10624382 | 2 |
| #26042133 | 2 |
| #26042130 | 2 |
| #26041786 | 2 |
| #1501 | 181 |