Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C2×#20238597 | C2 | semidirect |
| 3. #26045768 | C2 | semidirect |
| 4. #26045716 | C2 | semidirect |
| 5. #26045714 | C2 | semidirect |
| 6. #26045704 | C2 | semidirect |
| 7. C2×Q16×C373 | C2 | semidirect |
| 60. C373 | #452 | semidirect |
| 63. C2×Q16 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20238611 | 2 |
| C2×#20238597 | 2 |
| #26045768 | 2 |
| #26045716 | 2 |
| #26045714 | 2 |
| #26045704 | 2 |
| C2×Q16×C373 | 2 |
| #452 | 373 |