Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 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. #26042096 | C2 | semidirect |
| 2. #26041715 | C2 | semidirect |
| 3. C2×#19153760 | C2 | semidirect |
| 4. #26041094 | C2 | semidirect |
| 5. #26041085 | C2 | semidirect |
| 6. #26041063 | C2 | semidirect |
| 7. #472×C181 | C2 | semidirect |
| 90. C181 | #2193 | semidirect |
| 95. #472 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042096 | 2 |
| #26041715 | 2 |
| C2×#19153760 | 2 |
| #26041094 | 2 |
| #26041085 | 2 |
| #26041063 | 2 |
| #472×C181 | 2 |
| #2193 | 181 |