Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #26041332 | C2 | semidirect |
| 3. #26041012 | C2 | semidirect |
| 4. #382×C181 | C2 | semidirect |
| 6. #19153816 | C4 | semidirect |
| 7. #19153813 | C4 | semidirect |
| 12. C4×D724 | C4 | semidirect |
| 88. C181 | #1517 | semidirect |
| 92. #382 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041332 | 2 |
| #26041012 | 2 |
| #382×C181 | 2 |
| #1517 | 181 |