Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26041592 | C2 | direct (N × H) |
| 3. C2×#19153749 | C2 | semidirect |
| 4. C2×#19153736 | C2 | semidirect |
| 5. C2×C22⋊#13089678 | C2 | semidirect |
| 6. C22×C4⋊C4×C181 | C2 | semidirect |
| 14. #19153749 | C22 | semidirect |
| 15. #19153736 | C22 | semidirect |
| 16. C22⋊#13089678 | C22 | semidirect |
| 22. C2×C4⋊C4×C181 | C22 | semidirect |
| 90. C2×C181 | #480 | semidirect |
| 95. C181 | C2×#480 | semidirect |
| 98. C22×C4⋊C4 | D181 | semidirect |
| 114. C2×C4⋊C4 | C2×D181 | semidirect |
| 187. C2 | #26041592 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153790 | 2 |
| #26041592 | 2 |
| C2×#19153749 | 2 |
| C2×#19153736 | 2 |
| C2×C22⋊#13089678 | 2 |
| C22×C4⋊C4×C181 | 2 |
| C2×#480 | 181 |