Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 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×#19153805 | C2 | semidirect |
| 3. #26041180 | C2 | semidirect |
| 4. C42×Dic181 | C2 | semidirect |
| 5. C2×C4⋊Q8×C181 | C2 | semidirect |
| 25. C4×Dic181 | D4 | semidirect |
| 55. C4×C181 | #124 | semidirect |
| 62. C181 | #2858 | semidirect |
| 64. C2×C4⋊Q8 | D181 | semidirect |
| 119. C4 | #19153805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153813 | 2 |
| C2×#19153805 | 2 |
| #26041180 | 2 |
| C42×Dic181 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| #2858 | 181 |