Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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. #26041175 | C2 | semidirect |
| 5. #26041148 | C2 | semidirect |
| 6. #26041144 | C2 | semidirect |
| 9. #19153775 | C4 | semidirect |
| 29. C4⋊Dic181 | C2×C4 | semidirect |
| 34. C4×Dic181 | C2×C4 | semidirect |
| 62. C2×C4×C181 | C4⋊C4 | semidirect |
| 91. C181 | #2317 | semidirect |
| 154. C2×C4 | #15668428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153775 | 2 |
| #26041175 | 2 |
| #26041152 | 2 |
| #26041148 | 2 |
| #26041144 | 2 |
| C22×C4⋊C4×C181 | 2 |
| #2317 | 181 |