Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26041315 | C2 | semidirect |
| 4. #26041035 | C2 | semidirect |
| 8. C2×#15668433 | C4 | semidirect |
| 10. C22×#13089678 | C4 | semidirect |
| 74. C181 | #1812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153823 | 2 |
| #26041315 | 2 |
| #26041253 | 2 |
| #26041035 | 2 |
| #410×C181 | 2 |
| #1812 | 181 |