Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
322 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26041241 | C2 | semidirect |
| 3. C22⋊C8×D181 | C2 | semidirect |
| 4. #26041003 | C2 | semidirect |
| 5. #26041002 | C2 | semidirect |
| 6. #26041002 | C2 | semidirect |
| 7. #323×C181 | C2 | semidirect |
| 139. C181 | #1471 | semidirect |
| 147. #323 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153789 | 2 |
| #26041241 | 2 |
| C22⋊C8×D181 | 2 |
| #26041003 | 2 |
| #26041002 | 2 |
| #323×C181 | 2 |
| #1471 | 181 |