Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 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. #26041989 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041594 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041528 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041440 | C2 | semidirect |
| 9. #26041358 | C2 | semidirect |
| 10. #26041279 | C2 | semidirect |
| 11. C4×Q16×C181 | C2 | semidirect |
| 128. C181 | #3333 | semidirect |
| 138. C4×Q16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041989 | 2 |
| #26041951 | 2 |
| #26041626 | 2 |
| #26041594 | 2 |
| #26041574 | 2 |
| #26041528 | 2 |
| #26041479 | 2 |
| #26041440 | 2 |
| #26041358 | 2 |
| #26041279 | 2 |
| C4×Q16×C181 | 2 |
| #3333 | 181 |