Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×Dic362 | C2 | semidirect |
| 4. #26041629 | C2 | semidirect |
| 6. #26041562 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041386 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 116. C181 | #3369 | semidirect |
| 125. #462 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26042003 | 2 |
| #26041640 | 2 |
| #26041629 | 2 |
| #26041570 | 2 |
| #26041562 | 2 |
| #26041503 | 2 |
| #26041406 | 2 |
| #26041386 | 2 |
| C4×#15668436 | 2 |
| #462×C181 | 2 |
| #3369 | 181 |