Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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. #26042150 | C2 | semidirect |
| 4. #26042146 | C2 | semidirect |
| 17. #19153773 | C4 | semidirect |
| 19. C2×C4×Dic181 | C4 | semidirect |
| 20. C42×D181 | C4 | semidirect |
| 22. #117×C181 | C4 | semidirect |
| 102. C181 | #1827 | semidirect |
| 118. #117 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042265 | 2 |
| #26042258 | 2 |
| #26042150 | 2 |
| #26042146 | 2 |
| #26041747 | 2 |
| #1827 | 181 |