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×#19153846 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041658 | C2 | semidirect |
| 4. #26041535 | C2 | semidirect |
| 5. #26041486 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 7. #26041441 | C2 | semidirect |
| 8. #26041434 | C2 | semidirect |
| 9. C4×#15668437 | C2 | semidirect |
| 10. #26041357 | C2 | semidirect |
| 52. #15668437 | D4 | semidirect |
| 123. C4×C181 | #137 | semidirect |
| 134. C181 | #3276 | semidirect |
| 261. C4 | #19153846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153846 | 2 |
| D4×Dic362 | 2 |
| #26041658 | 2 |
| #26041535 | 2 |
| #26041486 | 2 |
| #26041484 | 2 |
| #26041441 | 2 |
| #26041434 | 2 |
| C4×#15668437 | 2 |
| #26041357 | 2 |
| #547×C181 | 2 |
| #3276 | 181 |