Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 10. #19153885 | C4 | semidirect |
| 11. #19153870 | C4 | semidirect |
| 15. #19153748 | C4 | semidirect |
| 16. #19153747 | C4 | semidirect |
| 17. #106×C181 | C4 | semidirect |
| 53. #13089678 | C42 | semidirect |
| 56. C8×C181 | C42 | semidirect |
| 75. C181 | #1776 | semidirect |
| 91. #106 | #10624382 | semidirect |
| 132. C8 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153885 | 2 |
| C2×#19153870 | 2 |
| C4⋊C4×#10624382 | 2 |
| #26042152 | 2 |
| #106×D181 | 2 |
| #1776 | 181 |