Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
140 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 8. C2×#15668452 | C4 | semidirect |
| 14. C2×#15668424 | C4 | semidirect |
| 15. C2×C16×C181 | C4 | semidirect |
| 62. C181 | #1375 | semidirect |
| 76. C2×C16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153891 | 2 |
| C2×#19153870 | 2 |
| C2×#19153755 | 2 |
| #1375 | 181 |