Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19153751 | C2 | semidirect |
| 3. C2×#19153743 | C2 | semidirect |
| 4. C2×#19153742 | C2 | semidirect |
| 5. #26041245 | C2 | semidirect |
| 6. C2×#19153726 | C2 | semidirect |
| 7. #408×C181 | C2 | semidirect |
| 11. C2×#15668439 | C4 | semidirect |
| 12. C2×#15668437 | C4 | semidirect |
| 13. C2×#15668436 | C4 | semidirect |
| 14. C2×#15668434 | C4 | semidirect |
| 119. C181 | #1975 | semidirect |
| 126. #408 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| C2×#19153751 | 2 |
| C2×#19153743 | 2 |
| C2×#19153742 | 2 |
| #26041245 | 2 |
| C2×#19153726 | 2 |
| #408×C181 | 2 |
| #1975 | 181 |