Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
344 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 72 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. #26042296 | C2 | semidirect |
| 2. #26042282 | C2 | semidirect |
| 3. #26042137 | C2 | semidirect |
| 6. #19153883 | C22 | semidirect |
| 7. #19153883 | C22 | semidirect |
| 100. C181 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042296 | 2 |
| #26042282 | 2 |
| #26042137 | 2 |
| C2×#19153812 | 2 |
| #1545 | 181 |