Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
680 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 378 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. C2×#19153871 | C2 | direct (N × H) |
| 4. C22×#13089685 | C4 | semidirect |
| 6. #19153871 | C22 | direct (N × H) |
| 12. C2×#13089685 | C2×C4 | semidirect |
| 24. #13089685 | C22×C4 | semidirect |
| 37. C22×C181 | #97 | semidirect |
| 46. C2×C181 | C2×#97 | semidirect |
| 50. C181 | C22×#97 | semidirect |
| 88. C22 | #19153871 | direct (N × H) |
| 97. C2 | C2×#19153871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13089685 | 2 |
| C2×#19153871 | 2 |
| C22×C4×Dic181 | 2 |
| C22×#97 | 181 |