Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
696 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 290 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. C4⋊C4×#10624382 | C2 | semidirect |
| 5. #19153895 | C4 | semidirect |
| 13. C2×C4⋊Dic181 | C4 | semidirect |
| 14. C2×#15668428 | C4 | semidirect |
| 15. C4⋊C4×D181 | C4 | semidirect |
| 17. C2×C4⋊C4×C181 | C4 | semidirect |
| 19. C4⋊#10624382 | C2×C4 | semidirect |
| 22. C4×#10624382 | C2×C4 | semidirect |
| 46. C2×Dic181 | C42 | semidirect |
| 51. C4×D181 | C42 | semidirect |
| 56. C2×C4×C181 | C42 | semidirect |
| 81. C181 | #2274 | semidirect |
| 95. C2×C4⋊C4 | #10624382 | semidirect |
| 138. C2×C4 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153895 | 2 |
| C4⋊C4×#10624382 | 2 |
| C4×C22⋊#10624382 | 2 |
| C2×C4⋊C4×D181 | 2 |
| #2274 | 181 |