Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 9. #19153870 | C4 | semidirect |
| 10. C4×#13089685 | C4 | semidirect |
| 11. C8×#10624382 | C4 | semidirect |
| 15. #19153727 | C4 | semidirect |
| 16. #19153726 | C4 | semidirect |
| 17. #97×C181 | C4 | semidirect |
| 60. C181 | #1726 | semidirect |
| 75. #97 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153870 | 2 |
| C4×D181⋊C8 | 2 |
| C2×C8×#10624382 | 2 |
| #26042215 | 2 |
| #97×D181 | 2 |
| #1726 | 181 |