Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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×#19153778 | C2 | semidirect |
| 3. #26041180 | C2 | semidirect |
| 4. C42×Dic181 | C2 | semidirect |
| 5. #384×C181 | C2 | semidirect |
| 8. #19153813 | C4 | semidirect |
| 18. C2×D724 | C2×C4 | semidirect |
| 24. C4×Dic181 | D4 | semidirect |
| 28. C42×C181 | C2×C4 | semidirect |
| 49. C4×C181 | C4×D4 | semidirect |
| 51. Dic181 | #127 | semidirect |
| 56. C181 | C4×#127 | semidirect |
| 61. #384 | D181 | semidirect |
| 85. C42 | C4×D181 | semidirect |
| 108. C4 | #19153778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| C2×#19153778 | 2 |
| #26041180 | 2 |
| C42×Dic181 | 2 |
| #384×C181 | 2 |
| C4×#127 | 181 |