Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #26041617 | C2 | semidirect |
| 3. #26041617 | C2 | semidirect |
| 4. #26041612 | C2 | semidirect |
| 5. #26041607 | C2 | semidirect |
| 6. #26041322 | C2 | semidirect |
| 7. #26041315 | C2 | semidirect |
| 8. #26041288 | C2 | semidirect |
| 9. C2×#19153740 | C2 | semidirect |
| 126. C181 | #3097 | 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 |
| #26041607 | 2 |
| #26041322 | 2 |
| #26041315 | 2 |
| #26041288 | 2 |
| C2×#19153740 | 2 |
| #26041246 | 2 |
| #536×C181 | 2 |
| #3097 | 181 |