Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041630 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 8. #26041490 | C2 | semidirect |
| 9. #26041387 | C2 | semidirect |
| 11. #446×C181 | C2 | semidirect |
| 116. C181 | #3369 | semidirect |
| 126. #446 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26042002 | 2 |
| #26041639 | 2 |
| #26041630 | 2 |
| #26041570 | 2 |
| #26041565 | 2 |
| #26041502 | 2 |
| #26041490 | 2 |
| #26041387 | 2 |
| C4×#15668438 | 2 |
| #446×C181 | 2 |
| #3369 | 181 |