Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26042143 | C2 | semidirect |
| 4. #26042142 | C2 | semidirect |
| 5. #26042141 | C2 | semidirect |
| 6. #26042140 | C2 | semidirect |
| 53. #13089678 | M16 | semidirect |
| 60. C8×C181 | M16 | semidirect |
| 77. C181 | #1569 | semidirect |
| 138. C8 | #15668458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042300 | 2 |
| #26042282 | 2 |
| #26042143 | 2 |
| #26042142 | 2 |
| #26042141 | 2 |
| #26042140 | 2 |
| M16×Dic181 | 2 |
| #1569 | 181 |