Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. #26041631 | C2 | semidirect |
| 5. #26041029 | C2 | semidirect |
| 6. #26041026 | C2 | semidirect |
| 7. #333×C181 | C2 | semidirect |
| 75. C181 | #1703 | semidirect |
| 82. #333 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041631 | 2 |
| #26041566 | 2 |
| #26041560 | 2 |
| #26041356 | 2 |
| #26041029 | 2 |
| #26041026 | 2 |
| #333×C181 | 2 |
| #1703 | 181 |