Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. C2×C8×#10624382 | C2 | semidirect |
| 4. #26042230 | C2 | semidirect |
| 5. #26042153 | C2 | semidirect |
| 6. #26042152 | C2 | semidirect |
| 21. #19153738 | C4 | semidirect |
| 22. #19153737 | C4 | semidirect |
| 23. #19153736 | C4 | semidirect |
| 24. #102×C181 | C4 | semidirect |
| 134. C181 | #1934 | semidirect |
| 157. #102 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153878 | 2 |
| C2×C8×#10624382 | 2 |
| #26042231 | 2 |
| #26042230 | 2 |
| #26042153 | 2 |
| #26042152 | 2 |
| #102×D181 | 2 |
| #1934 | 181 |