Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #26041144 | C2 | semidirect |
| 5. #26041047 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 7. #428×C181 | C2 | semidirect |
| 17. #19153742 | C4 | semidirect |
| 46. C4×Dic181 | C2×C4 | semidirect |
| 50. M16×C181 | C2×C4 | semidirect |
| 111. C181 | #1860 | semidirect |
| 114. #428 | D181 | semidirect |
| 154. M16 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041759 | 2 |
| C2×#19153742 | 2 |
| #26041278 | 2 |
| #26041144 | 2 |
| #26041047 | 2 |
| #26041038 | 2 |
| #428×C181 | 2 |
| #1860 | 181 |