Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26041408 | C2 | semidirect |
| 3. #26041406 | C2 | semidirect |
| 33. C2×#13089678 | Q8 | semidirect |
| 83. C181 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| #26041408 | 2 |
| #26041406 | 2 |
| #26041305 | 2 |
| #26041302 | 2 |
| #26041237 | 2 |
| #26041235 | 2 |
| C2×#19153726 | 2 |
| #424×C181 | 2 |
| #2961 | 181 |