Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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. #26042245 | C2 | semidirect |
| 4. #26042162 | C2 | semidirect |
| 9. C2×#15668458 | C4 | semidirect |
| 11. C22×#13089685 | C4 | semidirect |
| 18. #19153734 | C4 | semidirect |
| 19. #19153733 | C4 | semidirect |
| 20. #100×C181 | C4 | semidirect |
| 77. C181 | #1757 | semidirect |
| 95. #100 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153903 | 2 |
| #26042259 | 2 |
| #26042245 | 2 |
| #26042162 | 2 |
| #26041260 | 2 |
| #1757 | 181 |