Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
180 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 92 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. #26042142 | C2 | semidirect |
| 4. #26042140 | C2 | semidirect |
| 31. M16×C181 | C8 | semidirect |
| 49. C8×C181 | C2×C8 | semidirect |
| 66. C181 | #1565 | semidirect |
| 89. M16 | #13089685 | semidirect |
| 116. C8 | C2×#13089685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042295 | 2 |
| C2×C4⋊#13089685 | 2 |
| #26042142 | 2 |
| #26042140 | 2 |
| M16×Dic181 | 2 |
| #1565 | 181 |