Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041910 | C2 | semidirect |
| 3. #26041646 | C2 | semidirect |
| 4. #26041640 | C2 | semidirect |
| 5. #26041635 | C2 | semidirect |
| 6. #26041628 | C2 | semidirect |
| 7. #26041288 | C2 | semidirect |
| 10. #26041234 | C2 | semidirect |
| 11. C2×#103×C181 | C2 | semidirect |
| 127. C181 | #3137 | semidirect |
| 138. C2×#103 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041910 | 2 |
| #26041853 | 2 |
| #26041646 | 2 |
| #26041640 | 2 |
| #26041635 | 2 |
| #26041628 | 2 |
| #26041288 | 2 |
| #26041278 | 2 |
| #26041276 | 2 |
| #26041234 | 2 |
| C2×#103×C181 | 2 |
| #3137 | 181 |