Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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×C22⋊#13089678 | C2 | semidirect |
| 3. #26041015 | C2 | semidirect |
| 4. #26041012 | C2 | semidirect |
| 5. #381×C181 | C2 | semidirect |
| 6. C2×#15668449 | C4 | semidirect |
| 9. #19153795 | C4 | semidirect |
| 11. #19153790 | C4 | semidirect |
| 16. #19153775 | C4 | semidirect |
| 111. C181 | #1516 | semidirect |
| 115. #381 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041790 | 2 |
| C2×C22⋊#13089678 | 2 |
| #26041015 | 2 |
| #26041012 | 2 |
| #381×C181 | 2 |
| #1516 | 181 |