Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 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×#20238599 | C2 | semidirect |
| 2. C2×#20238598 | C2 | semidirect |
| 3. C2×#20238595 | C2 | semidirect |
| 4. #26045788 | C2 | semidirect |
| 5. #26045779 | C2 | semidirect |
| 6. #26045702 | C2 | semidirect |
| 7. C2×D8×C373 | C2 | semidirect |
| 29. #15688412 | D4 | semidirect |
| 37. C8×C373 | D4 | semidirect |
| 54. C373 | #496 | semidirect |
| 59. C2×D8 | D373 | semidirect |
| 92. C8 | C22⋊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 |
| C2×#20238595 | 2 |
| #26045788 | 2 |
| #26045779 | 2 |
| #26045702 | 2 |
| C2×D8×C373 | 2 |
| #496 | 373 |