Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26041687 | C2 | direct (N × H) |
| 35. C2×#13089678 | Q8 | semidirect |
| 49. C2×C8×C181 | Q8 | semidirect |
| 64. #13089678 | C2×Q8 | semidirect |
| 74. C8×C181 | C2×Q8 | semidirect |
| 88. C2×C181 | #501 | semidirect |
| 92. C181 | C2×#501 | semidirect |
| 133. C2×C8 | Dic362 | semidirect |
| 167. C8 | C2×Dic362 | semidirect |
| 181. C2 | #26041687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153815 | 2 |
| C2×#19153807 | 2 |
| #26041687 | 2 |
| C2×#19153749 | 2 |
| C2×#19153748 | 2 |
| C2×#19153747 | 2 |
| C2×#19153726 | 2 |
| C2×#107×C181 | 2 |
| C2×#501 | 181 |