Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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. #26041328 | C2 | semidirect |
| 4. #26041326 | C2 | semidirect |
| 5. C2×#19153751 | C2 | semidirect |
| 6. #108×D181 | C2 | semidirect |
| 7. #430×C181 | C2 | semidirect |
| 75. C181 | #2916 | semidirect |
| 81. #430 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042045 | 2 |
| C2×#19153824 | 2 |
| #26041328 | 2 |
| #26041326 | 2 |
| C2×#19153751 | 2 |
| #108×D181 | 2 |
| #430×C181 | 2 |
| #2916 | 181 |