Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
298 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 18. #19153740 | C4 | semidirect |
| 71. Q8×C181 | C4⋊C4 | semidirect |
| 109. C181 | #1865 | semidirect |
| 168. Q8 | #15668428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic181 | 2 |
| C2×#19153747 | 2 |
| C2×#19153740 | 2 |
| #26041175 | 2 |
| #26041042 | 2 |
| #26041033 | 2 |
| C2×#103×C181 | 2 |
| #1865 | 181 |