Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#20238610 | C2 | semidirect |
| 2. C2×#20238598 | C2 | semidirect |
| 3. C2×#20238595 | C2 | semidirect |
| 4. #26045715 | C2 | semidirect |
| 5. #26045712 | C2 | semidirect |
| 6. C22⋊#15688412 | C2 | semidirect |
| 7. #121×C373 | C2 | semidirect |
| 25. Dic746 | D4 | semidirect |
| 27. D1492 | D4 | semidirect |
| 64. C373 | #449 | semidirect |
| 69. #121 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238610 | 2 |
| C2×#20238598 | 2 |
| C2×#20238595 | 2 |
| #26045715 | 2 |
| #26045712 | 2 |
| C22⋊#15688412 | 2 |
| #121×C373 | 2 |
| #449 | 373 |