Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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. #19153871 | C4 | semidirect |
| 11. #19153870 | C4 | semidirect |
| 12. C8×#10624382 | C4 | semidirect |
| 15. #19153727 | C4 | semidirect |
| 16. #19153726 | C4 | semidirect |
| 17. #97×C181 | C4 | semidirect |
| 39. #13089685 | C42 | semidirect |
| 46. #13089678 | C42 | semidirect |
| 49. C8×C181 | C42 | semidirect |
| 55. #10624382 | #97 | direct (N × H) |
| 64. C181 | C4×#97 | semidirect |
| 81. #97 | #10624382 | direct (N × H) |
| 114. C8 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042238 | 2 |
| C2×#19153870 | 2 |
| C2×C8×#10624382 | 2 |
| C42×#10624382 | 2 |
| #97×D181 | 2 |
| C4×#97 | 181 |