Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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. #19153883 | C4 | semidirect |
| 10. C4⋊#13089685 | C4 | semidirect |
| 16. C4×#13089678 | C4 | semidirect |
| 17. C8×Dic181 | C4 | semidirect |
| 18. C8×Dic181 | C4 | semidirect |
| 19. C4×C8×C181 | C4 | semidirect |
| 24. C4⋊#10624382 | C8 | direct (N × H) |
| 57. #13089678 | C4⋊C4 | semidirect |
| 62. C8×C181 | C4⋊C4 | semidirect |
| 70. C4×C181 | C4×C8 | semidirect |
| 74. Dic181 | C4×C8 | semidirect |
| 82. C181 | C8×C4⋊C4 | semidirect |
| 101. C4×C8 | #10624382 | semidirect |
| 145. C8 | C4⋊#10624382 | direct (N × H) |
| 157. C4 | C8×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊(C4⋊C8) | 2 |
| C2×C8×#10624382 | 2 |
| C4×C4⋊#10624382 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| C4×C8×D181 | 2 |
| C8×C4⋊C4 | 181 |