Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
608 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 10. #19153723 | C4 | semidirect |
| 11. #95×C181 | C4 | semidirect |
| 43. C2×Dic181 | C4⋊C4 | semidirect |
| 49. C2×C4×C181 | C4⋊C4 | semidirect |
| 73. C181 | #1444 | semidirect |
| 85. #95 | #10624382 | semidirect |
| 123. C2×C4 | C4⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10624382 | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| #95×D181 | 2 |
| #1444 | 181 |