Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153807 | C2 | semidirect |
| 3. #26041588 | C2 | semidirect |
| 4. #26041584 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041577 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 8. #26041319 | C2 | semidirect |
| 9. #26041302 | C2 | semidirect |
| 135. C181 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153807 | 2 |
| #41×Dic181 | 2 |
| #26041588 | 2 |
| #26041584 | 2 |
| #26041581 | 2 |
| #26041577 | 2 |
| #26041321 | 2 |
| #26041319 | 2 |
| #26041302 | 2 |
| #26041280 | 2 |
| #417×C181 | 2 |
| #3080 | 181 |