Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 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. C2×#19153739 | C2 | direct (N × H) |
| 7. C22×Dic362 | C4 | semidirect |
| 12. #19153739 | C22 | direct (N × H) |
| 20. C2×Dic362 | C2×C4 | semidirect |
| 37. Dic362 | C22×C4 | semidirect |
| 52. C22×C181 | #103 | semidirect |
| 62. C2×C181 | C2×#103 | semidirect |
| 66. C181 | C22×#103 | semidirect |
| 119. C22 | #19153739 | direct (N × H) |
| 129. C2 | C2×#19153739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic362 | 2 |
| C23×#13089678 | 2 |
| C2×#19153739 | 2 |
| C22×C4⋊C4×C181 | 2 |
| C22×#103 | 181 |