Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153836 | C2 | semidirect |
| 2. C2×#19153824 | C2 | semidirect |
| 3. #26041860 | C2 | semidirect |
| 4. #26041857 | C2 | semidirect |
| 5. #26041528 | C2 | semidirect |
| 6. #26041524 | C2 | semidirect |
| 7. #26041519 | C2 | semidirect |
| 8. #26041514 | C2 | semidirect |
| 9. C2×#19153749 | C2 | semidirect |
| 10. #26041281 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 63. C2×#13089678 | D4 | semidirect |
| 152. C181 | #3061 | semidirect |
| 164. #417 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| C2×#19153824 | 2 |
| #26041860 | 2 |
| #26041857 | 2 |
| #26041528 | 2 |
| #26041524 | 2 |
| #26041519 | 2 |
| #26041514 | 2 |
| C2×#19153749 | 2 |
| #26041281 | 2 |
| #417×C181 | 2 |
| #3061 | 181 |