Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C2×C8×#10624382 | C2 | semidirect |
| 4. C4⋊C4×#10624382 | C2 | semidirect |
| 5. #26042153 | C2 | semidirect |
| 6. #26042152 | C2 | semidirect |
| 11. D4×#10624382 | C4 | semidirect |
| 17. #19153878 | C4 | semidirect |
| 23. #19153738 | C4 | semidirect |
| 24. #19153737 | C4 | semidirect |
| 25. #19153736 | C4 | semidirect |
| 26. #102×C181 | C4 | semidirect |
| 35. D181⋊C8 | C2×C4 | semidirect |
| 40. C4⋊#10624382 | C2×C4 | semidirect |
| 54. C2×#13089678 | C2×C4 | semidirect |
| 57. C4⋊Dic181 | C2×C4 | semidirect |
| 60. C2×C8×C181 | C2×C4 | semidirect |
| 61. C4⋊C4×C181 | C2×C4 | semidirect |
| 85. D724 | C42 | semidirect |
| 99. D4×C181 | C42 | semidirect |
| 123. #10624382 | #102 | direct (N × H) |
| 139. C181 | C4×#102 | semidirect |
| 164. #102 | #10624382 | direct (N × H) |
| 190. C2×C8 | C2×#10624382 | semidirect |
| 197. C4⋊C4 | C2×#10624382 | semidirect |
| 216. D4 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10624382 | 2 |
| C2×#19153878 | 2 |
| C2×C8×#10624382 | 2 |
| C4⋊C4×#10624382 | 2 |
| #26042153 | 2 |
| #26042152 | 2 |
| #102×D181 | 2 |
| C4×#102 | 181 |