Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 7. #19153885 | C4 | direct (N × H) |
| 12. C4×#13089678 | C4 | semidirect |
| 13. C8×Dic181 | C4 | semidirect |
| 14. C8×Dic181 | C4 | semidirect |
| 15. C4×C8×C181 | C4 | semidirect |
| 46. #13089678 | C42 | semidirect |
| 51. C8×C181 | C42 | semidirect |
| 59. C4×C181 | #107 | semidirect |
| 63. Dic181 | #107 | semidirect |
| 70. C181 | C4×#107 | semidirect |
| 85. C4×C8 | #10624382 | semidirect |
| 122. C8 | C4×#10624382 | semidirect |
| 133. C4 | #19153885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153885 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26042153 | 2 |
| C4×C8×D181 | 2 |
| C4×#107 | 181 |