Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19153815 | C2 | semidirect |
| 3. #26041640 | C2 | semidirect |
| 4. #26041637 | C2 | semidirect |
| 5. #26041628 | C2 | semidirect |
| 6. #26041624 | C2 | semidirect |
| 7. #26041281 | C2 | semidirect |
| 8. #26041280 | C2 | semidirect |
| 9. #26041278 | C2 | semidirect |
| 10. M16×Dic181 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 149. C181 | #3141 | semidirect |
| 160. #417 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041825 | 2 |
| C2×#19153815 | 2 |
| #26041640 | 2 |
| #26041637 | 2 |
| #26041628 | 2 |
| #26041624 | 2 |
| #26041281 | 2 |
| #26041280 | 2 |
| #26041278 | 2 |
| M16×Dic181 | 2 |
| #417×C181 | 2 |
| #3141 | 181 |