Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#19153740 | C2 | semidirect |
| 5. #26041042 | C2 | semidirect |
| 6. #26041041 | C2 | semidirect |
| 7. C2×#103×C181 | C2 | semidirect |
| 14. #19153792 | C4 | semidirect |
| 131. C181 | #1894 | semidirect |
| 136. C2×#103 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| C2×#19153792 | 2 |
| C2×#19153740 | 2 |
| #26041136 | 2 |
| #26041042 | 2 |
| #26041041 | 2 |
| C2×#103×C181 | 2 |
| #1894 | 181 |