Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 14. Q8×Dic181 | C4 | semidirect |
| 15. C4×Dic362 | C4 | semidirect |
| 16. #19153781 | C4 | semidirect |
| 19. C4×Q8×C181 | C4 | semidirect |
| 25. C4⋊#10624382 | Q8 | direct (N × H) |
| 48. Dic362 | C4⋊C4 | semidirect |
| 58. Q8×C181 | C4⋊C4 | semidirect |
| 73. C4×C181 | C4×Q8 | semidirect |
| 76. Dic181 | C4×Q8 | semidirect |
| 84. C181 | Q8×C4⋊C4 | semidirect |
| 96. C4×Q8 | #10624382 | semidirect |
| 128. Q8 | C4⋊#10624382 | direct (N × H) |
| 161. C4 | Q8×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| #26042230 | 2 |
| #26042225 | 2 |
| C4×C4⋊#10624382 | 2 |
| C4×Q8×D181 | 2 |
| Q8×C4⋊C4 | 181 |