Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #26042007 | C2 | semidirect |
| 3. #26041630 | C2 | semidirect |
| 4. #26041628 | C2 | semidirect |
| 5. #26041564 | C2 | semidirect |
| 6. #26041563 | C2 | semidirect |
| 9. C8×Dic362 | C2 | semidirect |
| 78. Dic362 | SD16 | semidirect |
| 118. C181 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042007 | 2 |
| D4×Dic362 | 2 |
| #26041630 | 2 |
| #26041628 | 2 |
| #26041564 | 2 |
| #26041563 | 2 |
| #26041484 | 2 |
| #26041482 | 2 |
| C8×Dic362 | 2 |
| #26041370 | 2 |
| C4×SD16×C181 | 2 |
| #3359 | 181 |