Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
436 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 154 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×C4×#13089685 | C2 | semidirect |
| 3. #26042145 | C2 | semidirect |
| 6. #19153873 | C4 | direct (N × H) |
| 18. C2×#13089685 | C2×C4 | semidirect |
| 29. C2×C4×D181 | C8 | semidirect |
| 30. C2×C4×D181 | C8 | semidirect |
| 82. C2×D181 | C4×C8 | semidirect |
| 85. C4×C181 | C22⋊C8 | semidirect |
| 87. Dic181 | C22⋊C8 | semidirect |
| 97. C181 | C4×C22⋊C8 | semidirect |
| 186. C4 | #19153873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153873 | 2 |
| C2×C4×#13089685 | 2 |
| #26042145 | 2 |
| C2×C42×D181 | 2 |
| C4×C22⋊C8 | 181 |