Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
128 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 41 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×#20238599 | C2 | semidirect |
| 2. C2×#20238598 | C2 | semidirect |
| 4. #26045757 | C2 | semidirect |
| 5. #26045721 | C2 | semidirect |
| 6. #26045712 | C2 | semidirect |
| 7. #102×C373 | C2 | semidirect |
| 23. Dic746 | D4 | semidirect |
| 50. Dic373 | SD16 | semidirect |
| 56. C373 | #460 | semidirect |
| 64. #102 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238599 | 2 |
| C2×#20238598 | 2 |
| #26045788 | 2 |
| #26045757 | 2 |
| #26045721 | 2 |
| #26045712 | 2 |
| #102×C373 | 2 |
| #460 | 373 |