Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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×Dic746 | C2 | semidirect |
| 3. #26045723 | C2 | semidirect |
| 4. #26045715 | C2 | semidirect |
| 6. C4×#15688412 | C2 | semidirect |
| 9. #20238598 | C4 | direct (N × H) |
| 21. Dic746 | C2×C4 | semidirect |
| 25. #15688412 | C2×C4 | semidirect |
| 40. C4×C373 | SD16 | semidirect |
| 49. C373 | C4×SD16 | semidirect |
| 92. C4 | #20238598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238598 | 2 |
| C4×Dic746 | 2 |
| #26045723 | 2 |
| #26045715 | 2 |
| #26045713 | 2 |
| C4×#15688412 | 2 |
| C4×D4×C373 | 2 |
| C4×SD16 | 373 |