Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. C22×#15668437 | C2 | semidirect |
| 3. C2×#19153804 | C2 | semidirect |
| 4. C2×#19153739 | C2 | semidirect |
| 5. C2×#19153736 | C2 | semidirect |
| 6. #26041034 | C2 | semidirect |
| 7. #390×C181 | C2 | semidirect |
| 133. C181 | #2012 | semidirect |
| 140. #390 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668437 | 2 |
| C22×#15668434 | 2 |
| C2×#19153804 | 2 |
| C2×#19153739 | 2 |
| C2×#19153736 | 2 |
| #26041034 | 2 |
| #390×C181 | 2 |
| #2012 | 181 |