Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19153864 | C2 | semidirect |
| 2. C2×#19153836 | C2 | semidirect |
| 3. #26041857 | C2 | semidirect |
| 4. #26041440 | C2 | semidirect |
| 5. #26041433 | C2 | semidirect |
| 6. #26041423 | C2 | semidirect |
| 7. #26041416 | C2 | semidirect |
| 8. #26041281 | C2 | semidirect |
| 9. C2×#19153740 | C2 | semidirect |
| 10. #26041247 | C2 | semidirect |
| 11. C2×#137×C181 | C2 | semidirect |
| 52. #15668449 | D4 | semidirect |
| 86. C2×Q8×C181 | D4 | semidirect |
| 169. C181 | #3013 | semidirect |
| 172. C2×#137 | D181 | semidirect |
| 233. C2×Q8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153864 | 2 |
| C2×#19153836 | 2 |
| #26041857 | 2 |
| #26041440 | 2 |
| #26041433 | 2 |
| #26041423 | 2 |
| #26041416 | 2 |
| #26041281 | 2 |
| C2×#19153740 | 2 |
| #26041247 | 2 |
| C2×#137×C181 | 2 |
| #3013 | 181 |