Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 612 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 |
|---|---|---|
| 1. C2×#19153875 | C2 | semidirect |
| 2. C2×#19153874 | C2 | semidirect |
| 3. #26042222 | C2 | semidirect |
| 12. C22×Dic362 | C4 | semidirect |
| 14. C22×C22⋊D181 | C4 | semidirect |
| 16. C22×C4×D181 | C4 | semidirect |
| 18. C23×C4×C181 | C4 | semidirect |
| 113. C181 | #1782 | semidirect |
| 128. C23×C4 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153875 | 2 |
| C2×#19153874 | 2 |
| #26042222 | 2 |
| C22×#15668449 | 2 |
| #1782 | 181 |