Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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. #26045725 | C2 | semidirect |
| 5. #26045716 | C2 | semidirect |
| 6. #26045715 | C2 | semidirect |
| 38. C22×C373 | Q16 | semidirect |
| 51. C373 | #467 | semidirect |
| 90. C22 | #20238600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238600 | 2 |
| C22×#15688412 | 2 |
| #26045771 | 2 |
| #26045725 | 2 |
| #26045716 | 2 |
| #26045715 | 2 |
| C22⋊Q8×C373 | 2 |
| #467 | 373 |