Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. C4×D181⋊C8 | C2 | semidirect |
| 3. C4×C4⋊#10624382 | C2 | semidirect |
| 4. #26042152 | C2 | semidirect |
| 9. #19153878 | C4 | direct (N × H) |
| 15. C4×D724 | C4 | semidirect |
| 16. D4×Dic181 | C4 | semidirect |
| 17. #19153778 | C4 | semidirect |
| 23. C4×D4×C181 | C4 | semidirect |
| 26. D181⋊C8 | C2×C4 | semidirect |
| 29. C4⋊#10624382 | C2×C4 | semidirect |
| 69. D724 | C42 | semidirect |
| 87. D4×C181 | C42 | semidirect |
| 109. C4×C181 | #102 | semidirect |
| 114. Dic181 | #102 | semidirect |
| 123. C181 | C4×#102 | semidirect |
| 138. C4×D4 | #10624382 | semidirect |
| 193. D4 | C4×#10624382 | semidirect |
| 237. C4 | #19153878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153878 | 2 |
| C4×D181⋊C8 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26042152 | 2 |
| C4×D4×D181 | 2 |
| C4×#102 | 181 |