Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19153748 | C2 | semidirect |
| 4. #26041149 | C2 | semidirect |
| 5. #336×C181 | C2 | semidirect |
| 74. C181 | #2094 | semidirect |
| 80. #336 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153748 | 2 |
| C2×#19153738 | 2 |
| #26041181 | 2 |
| #26041149 | 2 |
| #336×C181 | 2 |
| #2094 | 181 |