Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19153738 | C2 | semidirect |
| 3. #26041139 | C2 | semidirect |
| 4. #26041042 | C2 | semidirect |
| 5. C22×M16×C181 | C2 | semidirect |
| 9. #19153790 | C4 | semidirect |
| 45. C2×C8×C181 | D4 | semidirect |
| 104. C181 | #1895 | semidirect |
| 106. C22×M16 | D181 | semidirect |
| 144. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153790 | 2 |
| C2×#19153738 | 2 |
| #26041139 | 2 |
| #26041042 | 2 |
| C22×M16×C181 | 2 |
| #1895 | 181 |