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 |
|---|---|---|
| 2. #26041685 | C2 | direct (N × H) |
| 25. C2×#13089678 | Q8 | semidirect |
| 48. #13089678 | C2×Q8 | semidirect |
| 71. C2×C181 | #501 | semidirect |
| 75. C181 | C2×#501 | semidirect |
| 147. C2 | #26041685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153808 | 2 |
| #26041685 | 2 |
| C2×#19153749 | 2 |
| C2×#19153747 | 2 |
| C2×#19153727 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| C2×#501 | 181 |