Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 3. #26041322 | C2 | semidirect |
| 4. #26041319 | C2 | semidirect |
| 5. #26041315 | C2 | semidirect |
| 6. C2×#19153747 | C2 | semidirect |
| 8. #19153823 | C4 | semidirect |
| 26. #15668433 | C2×C4 | semidirect |
| 27. C2×#13089678 | C2×C4 | semidirect |
| 76. C181 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153823 | 2 |
| #26041762 | 2 |
| #26041322 | 2 |
| #26041319 | 2 |
| #26041315 | 2 |
| C2×#19153747 | 2 |
| #520×C181 | 2 |
| #2912 | 181 |