Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #26041174 | C2 | semidirect |
| 6. #26041148 | C2 | semidirect |
| 7. #26041145 | C2 | semidirect |
| 8. #26041144 | C2 | semidirect |
| 9. #384×C181 | C2 | semidirect |
| 13. #19153773 | C4 | semidirect |
| 44. #15668428 | C2×C4 | semidirect |
| 48. C4×Dic181 | C2×C4 | semidirect |
| 56. C42×C181 | C2×C4 | semidirect |
| 73. C4×D181 | C4⋊C4 | semidirect |
| 109. C181 | #2317 | semidirect |
| 117. #384 | D181 | semidirect |
| 166. C42 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153774 | 2 |
| C2×#19153773 | 2 |
| C2×C4⋊C4×D181 | 2 |
| #26041174 | 2 |
| #26041150 | 2 |
| #26041148 | 2 |
| #26041145 | 2 |
| #26041144 | 2 |
| #384×C181 | 2 |
| #2317 | 181 |