Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 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×#20238600 | C2 | semidirect |
| 4. #26045757 | C2 | semidirect |
| 5. #26045721 | C2 | semidirect |
| 7. #103×C373 | C2 | semidirect |
| 51. C373 | #464 | semidirect |
| 58. #103 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238600 | 2 |
| C2×#20238599 | 2 |
| #26045781 | 2 |
| #26045757 | 2 |
| #26045721 | 2 |
| #26045712 | 2 |
| #103×C373 | 2 |
| #464 | 373 |