Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. #26041626 | C2 | semidirect |
| 4. #26041624 | C2 | semidirect |
| 5. #26041569 | C2 | semidirect |
| 6. #26041568 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041477 | C2 | semidirect |
| 9. C8×Dic362 | C2 | semidirect |
| 10. #26041364 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 77. Dic362 | SD16 | semidirect |
| 91. Q8×C181 | #41 | semidirect |
| 125. C181 | #3362 | semidirect |
| 137. C4×SD16 | D181 | semidirect |
| 206. Q8 | #15668449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26041950 | 2 |
| #26041626 | 2 |
| #26041624 | 2 |
| #26041569 | 2 |
| #26041568 | 2 |
| #26041479 | 2 |
| #26041477 | 2 |
| C8×Dic362 | 2 |
| #26041364 | 2 |
| C4×SD16×C181 | 2 |
| #3362 | 181 |