Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26041305 | C2 | semidirect |
| 2. #26041288 | C2 | semidirect |
| 4. C2×#19153735 | C2 | semidirect |
| 6. #26041044 | C2 | semidirect |
| 100. C181 | #2046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041305 | 2 |
| #26041288 | 2 |
| #26041284 | 2 |
| C2×#19153735 | 2 |
| C2×#19153733 | 2 |
| #26041044 | 2 |
| C22×SD16×C181 | 2 |
| #2046 | 181 |