Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19153747 | C2 | semidirect |
| 4. #26041041 | C2 | semidirect |
| 11. C22⋊#13089678 | C4 | semidirect |
| 22. C2×#13089678 | C2×C4 | semidirect |
| 74. C22×C181 | #106 | semidirect |
| 96. C181 | #1853 | semidirect |
| 171. C22 | #19153747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153747 | 2 |
| C2×C22⋊#13089678 | 2 |
| #26041139 | 2 |
| #26041041 | 2 |
| C22×C4⋊C4×C181 | 2 |
| #1853 | 181 |