Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1068 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×#19153795 | C2 | semidirect |
| 2. #26041152 | C2 | semidirect |
| 3. #26041139 | C2 | semidirect |
| 6. C22×Dic362 | C22 | semidirect |
| 8. C2×C4⋊Dic181 | C22 | semidirect |
| 9. C2×#15668428 | C22 | semidirect |
| 12. #19153723 | C22 | semidirect |
| 26. C24×C181 | Q8 | semidirect |
| 58. C22×C181 | C22⋊Q8 | semidirect |
| 70. C181 | #2848 | semidirect |
| 90. C24 | Dic362 | semidirect |
| 129. C22 | #19153795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153795 | 2 |
| #26041152 | 2 |
| #26041139 | 2 |
| #26041135 | 2 |
| C24×C4×C181 | 2 |
| #2848 | 181 |