Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041630 | C2 | semidirect |
| 4. #26041621 | C2 | semidirect |
| 5. #26041575 | C2 | semidirect |
| 6. #26041525 | C2 | semidirect |
| 7. #26041485 | C2 | semidirect |
| 8. #26041420 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. #26041289 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 126. C181 | #3329 | semidirect |
| 137. #436 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| D4×Dic362 | 2 |
| #26041630 | 2 |
| #26041621 | 2 |
| #26041575 | 2 |
| #26041525 | 2 |
| #26041485 | 2 |
| #26041420 | 2 |
| C4×#15668438 | 2 |
| #26041289 | 2 |
| #436×C181 | 2 |
| #3329 | 181 |