Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041762 | C2 | semidirect |
| 2. #26041617 | C2 | semidirect |
| 3. #26041612 | C2 | semidirect |
| 4. #26041600 | C2 | semidirect |
| 5. #26041590 | C2 | semidirect |
| 6. #26041319 | C2 | semidirect |
| 7. C2×#19153749 | C2 | semidirect |
| 8. #26041280 | C2 | semidirect |
| 9. #26041275 | C2 | semidirect |
| 10. #26041246 | C2 | semidirect |
| 133. C181 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041762 | 2 |
| #26041617 | 2 |
| #26041612 | 2 |
| #26041600 | 2 |
| #26041590 | 2 |
| #26041319 | 2 |
| C2×#19153749 | 2 |
| #26041280 | 2 |
| #26041275 | 2 |
| #26041246 | 2 |
| #537×C181 | 2 |
| #3098 | 181 |