Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×D4×Dic181 | C2 | semidirect |
| 3. C2×#19153778 | C2 | semidirect |
| 4. C2×#19153776 | C2 | semidirect |
| 5. #26041181 | C2 | semidirect |
| 6. #26041179 | C2 | semidirect |
| 7. #26041148 | C2 | semidirect |
| 8. C42×Dic181 | C2 | semidirect |
| 9. #390×C181 | C2 | semidirect |
| 14. #19153812 | C4 | semidirect |
| 34. C2×D724 | C2×C4 | semidirect |
| 37. C2×C22⋊D181 | C2×C4 | semidirect |
| 52. C4×Dic181 | C2×C4 | semidirect |
| 53. C4×Dic181 | D4 | semidirect |
| 54. C4×Dic181 | D4 | semidirect |
| 58. C2×D4×C181 | C2×C4 | semidirect |
| 115. C4×C181 | C4×D4 | semidirect |
| 118. Dic181 | C4×D4 | semidirect |
| 119. Dic181 | #127 | semidirect |
| 127. C181 | C4×#127 | semidirect |
| 135. #390 | D181 | semidirect |
| 169. C2×D4 | C4×D181 | semidirect |
| 247. C4 | #19153776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153812 | 2 |
| C2×D4×Dic181 | 2 |
| C2×#19153778 | 2 |
| C2×#19153776 | 2 |
| #26041181 | 2 |
| #26041179 | 2 |
| #26041148 | 2 |
| C42×Dic181 | 2 |
| #390×C181 | 2 |
| C4×#127 | 181 |