Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#20238589 | C2 | semidirect |
| 4. #26045699 | C2 | semidirect |
| 7. C22×Dic373 | C4 | semidirect |
| 37. C22×C373 | C4⋊C4 | semidirect |
| 46. Dic373 | C22⋊C4 | semidirect |
| 53. C373 | #380 | semidirect |
| 91. C22 | #20238589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic373 | 2 |
| C2×#20238589 | 2 |
| C2×C22⋊Dic373 | 2 |
| #26045699 | 2 |
| C2×C22⋊C4×C373 | 2 |
| #380 | 373 |