Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#19153847 | C2 | semidirect |
| 2. C2×#19153822 | C2 | semidirect |
| 4. #26041853 | C2 | semidirect |
| 5. #26041536 | C2 | semidirect |
| 6. #26041528 | C2 | semidirect |
| 7. #26041519 | C2 | semidirect |
| 8. #26041511 | C2 | semidirect |
| 9. #26041319 | C2 | semidirect |
| 10. #26041276 | C2 | semidirect |
| 11. C2×#103×C181 | C2 | semidirect |
| 58. #15668433 | D4 | semidirect |
| 143. C181 | #3063 | semidirect |
| 155. C2×#103 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×#19153822 | 2 |
| #26041860 | 2 |
| #26041853 | 2 |
| #26041536 | 2 |
| #26041528 | 2 |
| #26041519 | 2 |
| #26041511 | 2 |
| #26041319 | 2 |
| #26041276 | 2 |
| C2×#103×C181 | 2 |
| #3063 | 181 |