Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
132 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 6. #19153887 | C4 | semidirect |
| 11. C2×#15668424 | C4 | semidirect |
| 14. C2×C16×C181 | C4 | semidirect |
| 56. C181 | #1382 | semidirect |
| 67. C2×C16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#108 | 2 |
| #26042289 | 2 |
| C2×C16×D181 | 2 |
| #1382 | 181 |