Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 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 |
|---|---|---|
| 1. C2×#19153749 | C2 | semidirect |
| 2. C2×#19153747 | C2 | semidirect |
| 6. #26041034 | C2 | semidirect |
| 7. #382×C181 | C2 | semidirect |
| 99. C181 | #2092 | semidirect |
| 106. #382 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153749 | 2 |
| C2×#19153747 | 2 |
| C2×#19153736 | 2 |
| #26041181 | 2 |
| #26041034 | 2 |
| #382×C181 | 2 |
| #2092 | 181 |