Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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. #26042014 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041640 | C2 | semidirect |
| 4. #26041626 | C2 | semidirect |
| 5. #26041568 | C2 | semidirect |
| 6. #26041564 | C2 | semidirect |
| 7. #26041496 | C2 | semidirect |
| 9. #26041409 | C2 | semidirect |
| 10. #26041388 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 124. C181 | #3373 | semidirect |
| 136. C4×SD16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042014 | 2 |
| D4×Dic362 | 2 |
| #26041640 | 2 |
| #26041626 | 2 |
| #26041568 | 2 |
| #26041564 | 2 |
| #26041496 | 2 |
| #26041474 | 2 |
| #26041409 | 2 |
| #26041388 | 2 |
| C4×SD16×C181 | 2 |
| #3373 | 181 |