Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
270 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 1. #26042260 | C2 | semidirect |
| 2. #26042184 | C2 | semidirect |
| 3. #26042183 | C2 | semidirect |
| 7. #19153875 | C22 | semidirect |
| 9. C2×D4×D181 | C4 | semidirect |
| 12. #19153805 | C4 | semidirect |
| 15. #19153773 | C4 | semidirect |
| 16. #124×C181 | C4 | semidirect |
| 84. C181 | #2128 | semidirect |
| 95. #124 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042260 | 2 |
| #26042184 | 2 |
| #26042183 | 2 |
| #26041847 | 2 |
| #2128 | 181 |